I personally feel that not everybody is shown on the map. However, JKR's statements certainly imply that yes, everybody is shown on the map.
If so, why did Rita Skeeter never appear on the map when she was marauding around Hogwarts as a beetle?
I personally feel that not everybody is shown on the map. However, JKR's statements certainly imply that yes, everybody is shown on the map.
If so, why did Rita Skeeter never appear on the map when she was marauding around Hogwarts as a beetle?
Skip to the bold paragraph for the summary.
As I pointed out in this answer, Professor Moody (Barty Crouch Jr.) confiscated the Marauder's map on the night of Harry's bath excursion. We can pretty precisely determine that this occurred on January 21st or January 28th.1 As I pointed out there, that is the first time we see Harry use the map in Goblet of Fire.
This right away explains why Rita wasn't seen on the map for the entire second half of the year — Harry didn't have it, and Moody probably wouldn't care even if he did check the map and happen to see her.
It is also perfectly sensible why Harry didn't see her on that very occasion. This was an excursion in the middle of the night, so there would be no reason for Rita scurrying around Hogwarts at that time.
That leaves the the beginning of the year through the end of January. As pointed out above, there is no mention of Harry using the map at all during that time. But even if we assume that Harry did use the map and it just wasn't mentioned, it would still be perfectly explainable why why there was never an issue of seeing Rita.
Firstly, Rita only came to Hogwarts to begin with because of the Triwizard Tournament. The Tournament didn't commence until Halloween, so she wouldn't have been at Hogwarts for the first two months of the year anyway. Her first appearance was shortly after the tournament began, at the weighing of the wands ceremony.
So now all we have left to contend with is November, December, and January. Now again there is no evidence suggesting that Harry even looked at the map during this time. But even if he had looked at it, he would have certainly only been looking at it occasionally. So even if Rita did happen to be scurrying around Hogwarts every so often, it is simply unlikely that it would have been precisely at the day and time that Harry was looking at the map. She only came to Hogwarts when there was a big event to report on, or if she needed to dig up some negative information about someone.
Now let's even assume that Harry did somehow see her on the map during one of those times. Would he have thought anything of it? He obviously knew that she was hanging around Hogwarts for various Tournament related stuff, so unless it was a particularly suspicious time or a particularly suspicious place, there wouldn't be anything strange about it. The instances that we do know that Rita was snooping around were all non-suspicious in both regards: She was on the grounds with Malfoy, at the Yule Ball, and at the Second Task.
Now we do have to consider the fact that she was banned from Hogwarts by Dumbledore:
"We'd have seen her in the garden!" said Ron. "Anyway, she's not supposed to come into school anymore, Hagrid said Dumbledore banned her...."
Harry Potter and the Goblet of Fire, chapter 24: "Rita Skeeter's Scoop"
However, it is unclear when this ban occurred. It doesn't seem to have been right away, because she was clearly welcomed at the weighing of the wands ceremony, and no one seemed to bat an eyelash at her appearance at the First Task (though it is possible that no one else saw her). Additionally, she apparently felt no compunction at brazenly appearing on the grounds even after she was banned, and Harry was aware of this:
"Who're you?" Hagrid asked Rita Skeeter as he slipped a loop of rope around the skrewt's sting and tightened it.
"Rita Skeeter, Daily Prophet reporter," Rita replied, beaming at him. Her gold teeth glinted.
"Thought Dumbledore said you weren' allowed inside the school anymore," said Hagrid, frowning slightly as he got off the slightly squashed skrewt and started tugging it over to its fellows.
Rita acted as though she hadn't heard what Hagrid had said.
Harry Potter and the Goblet of Fire, chapter 21:"The House-Elf Liberation Front"
So even if Harry had seen her on the map after she had been banned he probably still would not have found it particularly suspicious. He probably assumed that the ban was not such a big deal — after all she had no problem appearing in broad daylight, and Hagrid who knew about the ban didn't seem to care much.
It wasn't until Rita's article about Hagrid right after Christmas that the trio started getting suspicious about her sneaking around:
"How did that horrible Skeeter woman find out? You don't think Hagrid told her?"
"No," said Harry, leading the way over to the Gryffindor table and throwing himself into a chair, furious. "He never even told us, did he? I reckon she was so mad he wouldn't give her loads of horrible stuff about me, she went ferreting around to get him back."
"Maybe she heard him telling Madame Maxime at the ball," said Hermione quietly. "We'd have seen her in the garden!" said Ron. "Anyway, she's not supposed to come into school anymore, Hagrid said Dumbledore banned her...."
"Maybe she's got an Invisibility Cloak," said Harry, ladling chicken casserole onto his plate and splashing it everywhere in his anger. "Sort of thing she'd do, isn't it, hide in bushes listening to people."
Harry Potter and the Goblet of Fire, chapter 24: "Rita Skeeter's Scoop"
As seen above, this would have been only shortly before Harry lost the map, so there would not have been much time for him to see her and be suspicious.
Interestingly, when they became really suspicious after her article about Hermione, Hermione got confirmation from Moody that Rita had not been at the Second Task in an Invisibility Cloak:
"Well, Rita's definitely not using an Invisibility Cloak!" Hermione panted five minutes later, catching up with Harry and Ron in the entrance hall and pulling Harrys hand away from one of his wiggling ears so that he could hear her. "Moody says he didn't see her anywhere near the judges' table at the second task, or anywhere near the lake!"
Harry Potter and the Goblet of Fire, chapter 28: "The Madness of Mr. Crouch"
However, she never asked Moody if he had seen Rita on the map, and Moody never volunteered any such information.
So in summary, there was only a small window of time in which Harry had the map and Rita was frequenting Hogwarts. There is no evidence that Harry ever looked at the map during that time. If he had looked at the map, he probably would not have seen her anyway, and even if he had seen her he might not have found it suspicious.
1. This can be derived using the following premises:
The Second Task took place on February 24th.
"Well done, all of you!" said Ludo Bagman, bouncing into the tent and looking as pleased as though he personally had just got past a dragon. "Now, just a quick few words. You've got a nice long break before the second task, which will take place at half past nine on the morning of February the twenty-fourth — but we're giving you something to think about in the meantime!
Harry Potter and the Goblet of Fire, chapter 20: "The First task"
The First Task took place on November 24th.
"The first task will take place on November the twenty-fourth, in front of the other students and the panel of judges.
November 24th was a Tuesday.
The three of them would probably be happily imagining what deadly dangerous task the school champions would be facing on Tuesday.
February 24th will always be one weekday later than November 24th.
November has 30 days, December has 31 days, and January has 31 days. 31+31+6+24=92. 92/7=13.1428571428571429 and 1/7=.1428571428571429 so November 24th and February 24th are precisely thirteen weeks and one day apart.
February 24th was a Wednesday.
Wednesday is one day after Tuesday.
Harry went to Hogsmeade on January 16th or January 23rd.
There was a Hogsmeade visit halfway through January. Hermione was very surprised that Harry was going to go.
"I just thought you'd want to take advantage of the common room being quiet," she said. "Really get to work on that egg."
"Oh, I — I reckon I've got a pretty good idea what it's about now," Harry lied.
"Have you really?" said Hermione, looking impressed. "Well done!"
Harry's insides gave a guilty squirm, but he ignored them. He still had five weeks to work out that egg clue, after all, and that was ages... whereas if he went into Hogsmeade, he might run into Hagrid, and get a chance to persuade him to come back.
He, Ron, and Hermione left the castle together on Saturday and set off through the cold, wet grounds toward the gates.
Harry Potter and the Goblet of Fire, chapter 24: "Rita Skeeter's Scoop"
Five weeks before Wednesday February 24th would be Wednesday January 20th. The Saturday immediately after that would be January 23rd. This is based on the implication that the thought about "five weeks to go" took place before the Saturday mentioned in the following paragraph. On the other hand, "halfway through January" fits more with the previous Saturday which would have been January 16th. So we can assume the Hogsmeade visit was on one of those two Saturdays.
Harry's bath excursion occurred on the following Thursday.
On the way back from Hogsmeade they visited Hagrid:
Breaking into a run, she led them all the way back up the road, through the gates flanked by winged boars, and up through the grounds to Hagrid's cabin.
Harry Potter and the Goblet of Fire, chapter 24: "Rita Skeeter's Scoop"
The visit with Hagrid caused Harry to finally try Cedric's advice about the bath:
Lying to Hagrid wasn't quite like lying to anyone else. Harry went back to the castle later that afternoon with Ron and Hermione, unable to banish the image of the happy expression on Hagrid's whiskery face as he had imagined Harry winning the tournament. The incomprehensible egg weighed more heavily than ever on Harry's conscience that evening, and by the time he had got into bed, he had made up his mind — it was time to shelve his pride and see if Cedric's hint was worth anything.
Harry Potter and the Goblet of Fire, chapter 24: "Rita Skeeter's Scoop"
He implemented the plan on Thursday:
On Thursday night, Harry sneaked up to bed, put on the cloak, crept back downstairs, and, just as he had done on the night when Hagrid had shown him the dragons, waited for the portrait hole to open.
Harry Potter and the Goblet of Fire, chapter 25: "The Egg and the Eye"
The excursion took place on January 21st or January 28th.
This is simply Saturday January 16th plus five days or Saturday January 23rd plus five days.
Who says she didn't appear on the map?
As I recall, Rita Skeeter was at Hogwarts for most of Harry's fourth year, in order to cover the Triwizard Tournament. Seeing her hiding around the grounds wouldn't have been considered out of the ordinary. Even if her dot was in the middle of a bush or something, that wouldn't be too out-of-character for a predatory journalist.
It's never mentioned that Harry sees her name on the map, but that doesn't mean it wasn't on there somewhere. Hogwarts is a big place, and I don't think Harry uses the Marauders' Map more than once or twice that year. It's entirely possible for him not to have seen her, especially if he wasn't looking out for her.