Gilderoy Lockhart confessed the reality only in front of Harry and Co. Did the media ever learn the truth? The trio couldn't be credible sources to media, but they could at least tell the truth to Dumbledore (if Dumbledore already didn't know) or others who could spread the word.
Did the wizarding world ever learn that Gilderoy Lockhart was a fraud?
It doesn’t seem like the majority of the wizarding world learned that Lockhart was a fraud. When he’s in St. Mungo’s, Lockhart still receives lots of fan mail. It’d be unlikely if he’d been exposed as a fraud that so many people would be sending him large amounts of fan mail.
“I am not forgotten, you know, no, I still receive a very great deal of fan mail … Gladys Gudgeon writes weekly … I just wish I knew why …’ He paused, looking faintly puzzled, then beamed again and returned to his signing with renewed vigour. ‘I suspect it is simply my good looks …”
- Harry Potter and the Order of the Phoenix, Chapter 23 (Christmas on the Closed Ward)
In addition, the healers don’t say anything about him being a fraud who took credit for what other people did, and only say he had once been famous. They don’t show any indication of knowing.
“Listen to him,’ said the Healer, taking Lockhart’s arm and beaming fondly at him as though he were a precocious two-year-old. ‘He was rather well known a few years ago; we very much hope that this liking for giving autographs is a sign that his memory might be starting to come back.”
- Harry Potter and the Order of the Phoenix, Chapter 23 (Christmas on the Closed Ward)
Ron’s mother still uses her copy of Lockhart’s book on pests, which suggests she doesn’t know what went on, and implies she almost certainly doesn’t know Lockhart nearly Obliviated her son.
“Mrs Weasley was bending over to check the page on Doxys in Gilderoy Lockhart’s Guide to Household Pests, which was lying open on the sofa.”
- Harry Potter and the Order of the Phoenix, Chapter 6 (The Noble and Most Ancient House of Black)
It seems odd that she’d still be using the book (even though the Weasleys are poor) if she knew that the author was a fraud who tried to erase her son’s and his friend’s memories.
As you mention in the question, Lockhart explicitly admitted to Harry and Ron that he was a fraud. I don't think we find them sharing this with their peers, but it doesn't seem unlikely that they would have.
Additionally, there are many examples of Lockhart publicly demonstrating his ineptitude, such that those present (while perhaps not figuring out that he was a total fraud) might have caught on to the fact that he certainly wasn't quite the wizard he was made out to be. Some examples:
In the second years' very first lesson his attempt at subduing a pixie utterly fails.
He rolled up his sleeves, brandished his wand, and bellowed, "Peskipiksi Pesternomi!"
It had absolutely no effect; one of the pixies seized his wand and threw it out the window, too. Lockhart gulped and dived under his own desk, narrowly avoiding being squashed by Neville, who fell a second later as the chandelier gave way.
In response to this incident Harry says:
"Hermione, he didn't have a clue what he was doing –"
Surely other students noticed this at well. Of course, some like Hermione might have been blinded by his good looks, but as the year went on it is likely that even they realized what Lockhart truly was. As all first through fifth years and a good portion of sixth through seventh years take Defense Against the Dark Arts, most of the school was probably exposed to his incompetence in a classroom at some point during the year.
He failed to fix Harry's arm (and actually made it worse).
“Ah,” said Lockhart. “Yes. Well, that can sometimes happen. But the point is, the bones are no longer broken. That’s the thing to bear in mind. So, Harry, just toddle up to the hospital wing — ah, Mr. Weasley, Miss Granger, would you escort him? — and Madam Pomfrey will be able to — er — tidy you up a bit.”
In fact, in this case it appears that some students were openly skeptical of his abilities from the outset:
"Why can't I just go to the Hospital Wing?" said Harry through clenched teeth.
"He should really, Professor," said a muddy Wood, who couldn't help grinning even though his seeker was injured.
He made a fool of himself at the dueling club.
First he was roundly defeated by Snape:
Both of them swung their wands above their heads and pointed them at their opponent; Snape cried: "*Expelliarmus!" There was a dazzling flash of scarlet light and Lockhart was blasted off his feet: He flew backward off the stage, smashed into the wall, and slid down it to sprawl on the floor.
Later he is ineffective at dealing with Malfoy's snake:
"Allow me!" shouted Lockhart. He brandished his wand at the snake and there was a loud bang; the snake, instead of vanishing, flew ten feet into the air and fell back to the floor with a loud smack. Enraged, hissing furiously, it slithered straight toward Justin Finch-Fletchley and raised itself again, fangs exposed, poised to strike.
Based on the above public spectacles, it is highly possible that most or all of the students suspected that Lockhart wasn't quite who he claimed to be. These students may have also spread the word to their families (who may or may not have believed them).
Additionally, it would seem that many of the staff were aware of Lockhart's ineptitude:
Madame Pomfrey explicitly referred to Lockhart as inept after he removed the bones from Harry's arm.
Still tut-tutting about dangerous sports and inept teachers, Madam Pomfrey retreated, leaving Ron and Hermione to help Harry gulp down some water.
Similarly, in the beginning of Prisoner of Azkaban when Harry fainted from the Dementor, Madam Pomfrey again insinuated that Lockhart was sub-par:
"Did he, now?" said Madam Pomfrey approvingly. "so we've finally got a Defense Against the Dark Arts teacher who knows his remedies?"
It seems that Dumbledore was at least somewhat aware of Lockhart's chicanery.
First of all, he's Dumbledore. As Harry so eloquently said at the end of Philosopher's Stone:
I think he knows more or less everything that goes on here, you know.
Furthermore, Dumbledore's comment to Lockhart at the end of Chamber of Secrets seems to indicate that he was aware of something:
"He tried to do a Memory Charm and the wand backfired," Ron explained quietly to Dumbledore.
"Dear me," said Dumbledore, shaking his head, his long silver mustache quivering. "Impaled upon your own sword, Gilderoy!"
He was clearly wrong about Mrs. Norris.
In the presence of Dumbledore, McGonagall, and Snape (as well as Harry, Ron, and Hermione) Lockhart stated:
"It was definitely a curse that killed her – probably the Transmogrifian Torture – I've seen it used many times, so unlucky I wasn't there, I know the very countercurse that would have saved her...."
This was shown to be incorrect several moments later:
At last Dumbledore straightened up.
"She's not dead, Argus," he said softly.
By the end of Chamber of Secrets it seems that all the teachers had caught on.
Witness the scene in the staffroom where all the teachers seem to be poking fun at Lockhart's alleged exploits, and specifically McGonagall's comment once Lockhart leaves:
The staff room door banged open again. For one wild moment, Harry was sure it would be Dumbledore. But it was Lockhart, and he was beaming.
“So sorry — dozed off — what have I missed?”
He didn’t seem to notice that the other teachers were looking at him with something remarkably like hatred. Snape stepped forward.
“Just the man,” he said. “The very man. A girl has been snatched by the monster, Lockhart. Taken into the Chamber of Secrets itself. Your moment has come at last.”
Lockhart blanched.
“That’s right, Gilderoy,” chipped in Professor Sprout. “Weren’t you saying just last night that you’ve known all along where the entrance to the Chamber of Secrets is?”
“I — well, I —” sputtered Lockhart.
“Yes, didn’t you tell me you were sure you knew what was inside it?” piped up Professor Flitwick.
“D-did I? I don’t recall —”
“I certainly remember you saying you were sorry you hadn’t had a crack at the monster before Hagrid was arrested,” said Snape. “Didn’t you say that the whole affair had been bungled, and that you should have been given a free rein from the first?”
Lockhart stared around at his stony faced colleagues.
“I — I really never — you may have misunderstood —”
“We’ll leave it to you, then, Gilderoy,” said Professor McGonagall. “Tonight will be an excellent time to do it. We’ll make sure everyone’s out of your way. You’ll be able to tackle the monster all by yourself. A free rein at last.”
Lockhart gazed desperately around him, but nobody came to the rescue. He didn’t look remotely handsome anymore. His lip was trembling, and in the absence of his usually toothy grin, he looked weak chinned and feeble.
“V-very well,” he said. “I’ll — I’ll be in my office, getting — getting ready.”
And he left the room.
“Right,” said Professor McGonagall, whose nostrils were flared, “that’s got him out from under our feet.
It is even possible that Umbridge (and by extension the Ministry) was somewhat aware of Lockhart's incompetence.
When Umbridge describes their previous teachers in the first Defense Against the Dark Arts lesson in Order of the Phoenix she says:
"I do not wish to criticize the way things have been run in this school," she said, an unconvincing smile stretching her wide mouth, "but you have been exposed to some very irresponsible wizards in this class, very irresponsible indeed – not to mention," she gave a nasty little laugh, "extremely dangerous half-breeds."
In fairness, though, Umbridge's definition of irresponsible may simply mean allowing magic to be done.
Hagrid explicitly disbelieved Lockhart's tales, and criticized him.
When Harry, Ron, and Hermione visit Hagrid for help with Ron's slug problem, Lockhart is leaving as they arrive. When Harry asks Hagrid about Lockhart's visit, we are told:
"Givin' me advice on gettin' kelpies out of a well," growled Hagrid, moving a half-plucked rooster off his scrubbed table and setting down the teapot. "Like I don' know. An' bangin' on about some banshee he banished. If one word of it was true, I'll eat my kettle."
It was most unlike Hagrid to criticize a Hogwarts teacher, and Harry looked at him in surprise.
This is especially noteworthy because this occurred at the beginning of the school year before Lockhart had had much time to publicly make a fool of himself.
It thus appears that both the students and staff of Hogwarts were well aware that Lockhart was something of a fraud. This knowledge may or may not have spread even beyond the confines of Hogwarts. There doesn't seem to be any mention, though, of anyone specifically knowing that all of Lockhart's books were lies. Indeed, in Order of the Phoenix when the Daily Prophet specifically criticizes Dumbledore's staff choices, it mentions issues with Lupin, Hagrid, and Moody, but says nothing about Lockhart:
“Among those ‘eccentric decisions’ are undoubtedly the controversial staff appointments previously described in this newspaper, which have included the hiring of werewolf Remus Lupin, half giant Rubeus Hagrid, and delusional ex-Auror ‘Mad-Eye’ Moody.
If Lockhart's fraudulence was widely known in the greater wizarding world, the Prophet would likely have mentioned it as well.
You write
The trio couldn't be credible sources to media, but they could at least tell the truth to Dumbledore (if Dumbledore already didn't know) or others who could spread the word.
According to Pottermore, Dumbledore knew that Lockhart was a fraud:
Albus Dumbledore’s plans, however, ran deep. He happened to have known two of the wizards for whose life’s work Gilderoy Lockhart had taken credit, and was one of the only people in the world who thought he knew what Lockhart was up to. Dumbledore was convinced that Lockhart needed only to be put back into an ordinary school setting to be revealed as a charlatan and a fraud. Professor McGonagall, who had never liked Lockhart, asked Dumbledore what he thought students would learn from such a vain, celebrity-hungry man. Dumbledore replied that ‘there is plenty to be learned even from a bad teacher: what not to do, how not to be’.
So Dumbledore not only thinks it is acceptable to hire someone as a teacher who is not qualified at teaching, he even thinks that having Lockhart in school will somehow reveal Lockhart as a charlatan and a fraud. How that was supposed to work is anyone's guess.
Even Hermione, who is described as a rational girl, has a crush on him:
‘Why,’ demanded Ron, seizing her timetable, ‘have you outlined all Lockhart’s lessons in little hearts?’
Hermione snatched the timetable back, flushing furiously. (CoS)
While the boys were not impressed with the test about Lockhart, Hermione thinks there is nothing wrong:
Ron was now staring at Lockhart with an expression of disbelief on his face; Seamus Finnigan and Dean Thomas, who were sitting in front, were shaking with silent laughter. Hermione, on the other hand, was listening to Lockhart with rapt attention (CoS)
And a little later, immediately after the incident with the Cornish pixies, Hermione still defends him:
‘Can you believe him?’ roared Ron, as one of the remaining pixies bit him painfully on the ear.
‘He just wants to give us some hands-on experience,’ said Hermione, immobilising two pixies at once with a clever Freezing Charm and stuffing them back into their cage. (CoS)
While Hermione later lost her admiration for Lockhart, it is likely that others didn't, because humans have a tendency to keep their opinions regardless of facts.
One example of this is Mrs Weasley. Even though she must have heard from Ron that Lockhart tried to erase his memory and stop the rescue mission for her daughter, she still uses his book. Worse yet, the information there is probably useless, as Lockhart regularly mentions spells that don't exist or are not suited for the given purpose. But a charming smile is more important than his character or whether the facts mentioned in his book are useful.
Mrs Weasley was bending over to check the page on Doxys in Gilderoy Lockhart’s Guide to Household Pests, which was lying open on the sofa. (OotP)
So it's safe to assume that a significant part of the students were convinced that Lockhart was at least incompetent, while the other part would rationalize to themselves why he behaved that way, like Hermione does in the beginning. To consider him incompetent doesn't mean to assume that he erased other people's memory. It is even possible to assume that he is average in normal situations, but rises to a challenge in life or death situations, as Harry does at the end of each of the books.
Parents hearing from their children would probably discount it as badmouthing a teacher because they don't like him or he demands too much or something similar. Lockhart still receives a lot of fan mail, so it is clear that it wasn't generally known that Lockhart was a fraud, despite Dumbledore's plan to reveal him as such.
