These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
One moment that could be this or (even more) Hilarious in Hindsight is the passage in the Christmas chapter describing the Weasley Twins enchanting snowballs to bounce off the back of Professor Quirell's turban after you've read the end of the book and discovered what he's keeping under there.
Another passage involves Hagrid forbidding Harry to buy a solid-gold cauldron. Imagine if Harry did buy that kind of cauldron, y'know, for Potions class...
Dumbledore, when asked by Harry about what he sees in the Mirror of Erised, amusingly replies that he sees himself holding a new pair of socks. Word of God after the seventh book has confirmed that he was lying; what he actually sees is his dead sister Ariana alive and well, and his estranged brother Aberforth having forgiven him.
Rereading the opening of this book with Dumbledore telling McGonagall about how little they have had to celebrate for 11 years... and with the knowledge of how bad things were under Voldemort was when he was in charge in Deathly Hallows...
It Gets Better: Notably, It takes about a third of the novel before Harry gets to Hogwarts. And quite a few children readers were turned off by the first few chapters for being too slow-paced; not to mention most of Rowling's dry satire on middle-class insecurities flying straight over their heads.
Special Effect Failure: Some of the owls in the Privet Drive sequence are stuffed/fake. They look good and they cut away fast to hide it, but they aren't moving.
Ship-to-Ship Combat: Probably few people realized just how big and vicious of a battle this book would begin among its fans, most prominently among Harry/Hermione and Ron/Hermione shippers.
Squick: Dumbledore's experience with the Every Flavor Beans. He lost his liking to them a long time ago because of a vomit-flavored one, and when we see him actually try another, it was earwax-flavored.
Viewers Are Morons: The infamous change in the title for the American market, on the basis that Americans couldn't possibly take any interest in the book unless there was an explicit reference to magic.
What an Idiot: Hagrid takes Harry, Ron (only in the film), Neville, Hermione and Malfoy into the Forbidden Forrest to look for a Unicorn Murderer for detention. Harmful to Minors does not begin to describe Hagrid.
Vernon insults magic and threatens Harry in front of Hagrid, a half-giant with super strength, who happens to be from the wizarding world. It's a good thing Hagrid isn't malicious, or Vernon would've probably ended up with a broken neck, or worse.
The Woobie: Harry is this at the beginning of the film for living with family members who are abusive towards him.