What did Hagrid do to Mrs. Norris/Filch?

Hagrid Breaks Rules and Mrs. Norris Reports Rule Breakers to Filch

I believe the passage that the wiki is referencing occurs quite early in the series, in Chapter 8 ("The Potions Master") of Harry Potter and the Philosopher's Stone.

Harry and Ron were delighted to hear Hagrid call Filch "that old git." "An' as fer that cat, Mrs. Norris, I'd like ter introduce her to Fang sometime. D'yeh know, every time I go up ter the school, she follows me everywhere? Can't get rid of her -- Filch puts her up to it."

Earlier in that same chapter, we get what I believe is the first description of Mrs. Norris.

Filch owned a cat called Mrs. Norris, a scrawny, dust-colored creature with bulging, lamplike eyes just like Filch's. She patrolled the corridors alone. Break a rule in front of her, put just one toe out of line, and she'd whisk off for Filch, who'd appear, wheezing, two seconds later.

So we can see that Mrs. Norris reports rule breaking to Filch. This is all in the first book, before any that Chamber of Secrets business, so I don't think we can assume that Mrs. Norris trails Hagrid just because he's suspected of opening the Chamber of Secrets. But we do see Hagrid breaking wizarding rules fairly early on -- for example, by using an umbrella as a wand and by keeping a baby dragon (Norbert) at his hut. It seems reasonable to infer from this information that Mrs. Norris is trailing Hagrid in order to catch him breaking a rule (perhaps especially in relation to keeping magical creatures, since that is something that Hagrid does quite a bit) so she can report this to Filch.

As for why Filch doesn't treat the other professors this way, it is unclear, but I would venture two possibilities:

1. The other professors don't flout rules as often or openly as Hagrid. I don't think that we see most of the professors who are regulars in the books flout the rules as often as Hagrid. Hagrid's preferred method of breaking the rules (hiding magical creatures) also seems more likely to result in detection than many others would be.

2. Hagrid isn't a professor at this point whereas the others are. Professor is arguably a higher position in the hierarchy of Hogwarts staff than Filch's role are caretaker whereas Hagrid's role as groundskeeper arguably isn't. Filch might be less likely to censure a professor because the professors have higher positions than him.

I'm not sure there is always a reason for Filch to specifically dislike someone. He's a squib, too wizard for muggle-town, too muggle for wizard-town. It's tacitly accepted that he has no place in society (he's probably only got a job because Dumbledore always reaches out to these margianlised groups). Years of being on the outside has lead him to be a bitter man, so he uses what little authority he's got to lash out at the society that's never accepted him.

This is important because it's where Filch's character comes from, it's why he is how he is. Just by being born wizards, all of the students have a higher status than him. Regardless of what he achieves. It's largely unspoken, but the prejudice is always there.

Hagrid, of course, likes the students anyway, and doesn't like how Filch treats them. He stands up for what he believes is right, regardless of any mitigating factors around Filch and his upbringing.

So this is probably the reason for the tension between the two, who responded to their 'outsider' status in two very different ways.

It helps to understand the reference; Mrs. Norris is from Mansfield Park. The basics is that Mrs. Norris is an insecure, bitter person who takes out her frustrations on the few people who are lower in status than she is. Filch is a Squib. Who is lower in the social rankings than he? Kids who aren't allowed to do magic. That's why he is so mean to them, and always looking for an excuse to put them down. Hagrid doesn't use a wand, so he's pretty much in the same class, but Filch would never show disrespect to the real magic teachers, because they are his betters, and he knows it. The cat is just mirroring Filch's attitude.