I've done a thorough trawl through the books, including Fantastic Beasts and Where to Find Them, in search of all the plants and animals which Lovegood believes in. I've tried my best to make the answer exhaustive. There remains some doubts about someSome of the plants and animals which are only mentioned in passing and whose existence cannotso it's not possible to be definitively provendefinitive on whether or disprovennot they exist. I've included entries which are mentioned by Luna Lovegood too since she often touts the beliefs of her father. I've also included creatures and objects referenced in The Quibbler.
My conclusion: not everything Lovegood believes in is nonsense, although some of it is. At least six things mentioned by Xenophilius Lovegood definitely exist. Naturally, it's much harder to find real things which are not believed in by the rest of the magical community.
The question seems to be looking for things which Lovegood believes is real but nobody else does. Naturally, these examples are much harder to find. I've evaluated in each instance whether it's likely that the creature or plant is real, and whether its existence is taken seriously by the public at large.
The Wrackspurt is another creature which seems likely to be a part of the Lovegoods' imagination. When Harry is lost in thought about being the Chosen One...
"You all right, Harry? You look funny," said Neville.
Harry started.
"Sorry - I -"
"Wrackspurt got you?" asked Luna sympathetically, peering at Harry through her enormous coloured spectacles.
"I - what?"
"A Wrackspurt...they're invisible, they float in through your ears and make your brain go fuzzy," she said. "I thought I felt one zooming around in here."
She flapped her hands at thin air, as though beating off large invisible moths. Harry and Neville caught each other's eye and hastily began to talk of Quidditch.
(Half-Blood Prince, Chapter 7, The Slug Club).
Harry and Neville certainly seem to find the concept of the Wrackspurt ridiculous, as did Victor Krum.
"That's her," he said, pointing at Luna, who was still dancing alone, waving her arms around her head like someone attempting to beat off midges.
"Vy is she doing that?" asked Krum.
"Probably trying to get rid of a Wrackspurt," said Harry, who recognised the symptoms.
Krum did not seem to know whether or not Harry was making fun of him.
(Deathly Hallows, Chapter 8, The Wedding).
I think that this is enough to conclude that Wrackspurts are fictitious. Nobody else has heard of them and they can be confused for a simple dazed expression. The fact that they are supposed to be invisible doesn't add to their credibility.
Things we can't be sure of, or about which there is insufficient information.
There is only one mention of moon frogs in the books, in The Quibbler:
...an interview with a wizard who claimed to have flown to the moon on a Cleandweep Six and brought back a bag of moon frogs to prove it...
(Order of the Phoenix, Chapter 10, Luna Lovegood)*.
Perhaps the claim of reaching the moon on a broom isn't as ludicrous as it sounds but it is still pretty unlikely. We have no source of frogs living on the moon outside of The Quibbler so have no real way of verifying the claim. We know that Harry finds the claim unlikely but that doesn't really confirm whether they existed or not (Harry is ignorant about an awful lot). We also don't know whether the wizarding community believed in moon frogs or not. People might think that moon frogs are real but find the idea of flying to the moon ridiculous. I think this one is open to interpretation.
Again, the Umgubular Slashkiltor is only mentioned once, by Luna.
"Well, my dad is very supportive of any anti-Ministry action!" said Luna Lovegood proudly from just behind Harry; evidently she had been eavesdropping on his conversation while Justin Finch-Fletchley attempted to disentangle himself from the robes that had flown up over his head. "He's always saying he'd believe anything of Fudge; I mean, the number of goblins Fudge has had assassinated! And of course he uses the Department of Mysteries to develop terrible poisons, which he secretly feeds to anybody who disagrees with him. And then there's his Umgubular Slashkilter -"
"Don't ask," Harry muttered to Cho as she opened her mouth, looking puzzled. She giggled.
(Order of the Phoenix, Chapter 18, Dumbledore's Army).
The Lexicon thinks that the Slashkilter may be a creature, and I'm inclined to agree with them. However, it could also be an object or a weapon; it isn't altogether clear from the context.
From Cho's reaction we could easily surmise that the Slashkilter is not widely known about or believed in in the magical community. We don't really have enough information to make an informed call on the Slashkilter.
Luna mentions these when describing the Gurdyroot in the quote above.
"Oh, it's a Gurdyroot," she said, stuffing the cat litter and the toadstool back in her bag. "You can keep it if you like, I've got a few of them. They're really excellent for warding off Gulping Plimpies."
(Half-Blood Prince, Chapter 20, Lord Voldemort's Request).
Now we know that Plimpies exist, based on the Fantastic Beasts entry cited above. However, it does specifically say there that Plimpies are an underwater creature. Luna seems to be carrying around the Gurdyroot when walking around overground in order to protect herself from these Gulping Plimpies. This makes me strongly suspect that they are a fictitious animal and that Luna is acting on superstition, not evidence. On this basis, it's likely that nobody else took the Gulping Plimpy seriously. They are only mentioned once, and very briefly, so I'm not sure we can be definitive.
Again, these are only mentioned once.
The place was quite empty, except for a few desks and, in the very middle of the room, an enormous glass tank of deep green liquid, big enough for all of them to swim in; a number of pearly-white objects were drifting around lazily in it.
"What're those things?" whispered Ron.
"Dunno," said Harry.
"Are they fish?" breathed Ginny.
"Aquavirius Maggots!" said Luna excitedly. "Dad said the Ministry were breeding -"
"No," said Hermione. She sounded odd. She moved forward to look through the side of the tank. "They're brains."
(Order of the Phoenix, Chapter 34, The Department of Mysteries).
The maggots are a good candidate for a fictitious creature. Nobody else mentions them and Luna doesn't even seem to be able to identify them. The items in the tank are confirmed to be brains, after all, so the fact that Luna jumps to conclusions so rapidly is probably suggestive. They also fit well into Xenophilius's world of government conspiracy theories. Still, we have no firm statement saying they're fictional.
These are only mentioned in one chapter, by Luna again.
"Mistletoe," said Luna dreamily, pointing at a large clump of white berries placed almost over Harry's head. He jumped out from under it. "Good thinking," said Luna very seriously. "It's often infected with Nargles."
Harry was saved the necessity of asking what Nargles were by the arrival of Angelina, Katie and Alicia.
(Order of the Phoenix, Chapter 21, The Eye of the Snake).
It's clear that Harry has never heard of Nargles and doesn't believe in them. Cho seemed to be similarly confused.
"Mistletoe," said Cho quietly, pointing at the ceiling over his head.
"Yeah," said Harry. His mouth was very dry. "It's probably full of Nargles, though."
"What are Nargles?"
"No idea," said Harry. She had moved closer. His brain seemed to have been Stunned. "You'd have to ask Loony. Luna, I mean."
Cho made a funny noise halfway between a sob and a laugh.
(Order of the Phoenix, Chapter 21, The Eye of the Snake).
Clearly she's never heard of them either. I think this is another case where the creature probably isn't real but it isn't possible to completely rule it out.
All in all, there are eight things which the Lovegoods believe in which are real and which are widely accepted (even if in two cases we can't be definitive that anybody else does), four things which they believe in which don't exist and five things about which we can't be sure. It's a mixed bag but it does at least show that not everything Xenophilius Lovegood believed in was absurd.