The picture of Harry and Lockhart has the former walking away from the frame, leaving the latter looking dejected.
Professor Lockhart's Valentine's Day celebration:
Lockhart: Why not ask Professor Snape to show you how to whip up a love potion!
Snape was looking as if the first person to ask him for a love potion would be force-fed poison.
Made funnier by the fact that Love Potions are banned at Hogwarts.
And the fact that Snape probably would feed poison to anyone who asked. We can assume that no one did.
Flitwick apparently knows a thing or two about love charms, and is not happy to hear Lockhart announcing that.
The school is being swept with gossip that Harry is the Heir of Slytherin: most students treat Harry like he's radioactive, but Fred and George ridicule the entire idea. "Make way for the heir of Slytherin, seriously evil wizard coming through!"
"Soon the air was thick with flying gnomes."
"... the gnome, sensing weakness, sank its razor-sharp teeth into Harry's hand. He had a hard job shaking it off until- "Wow, Harry! That must've been fifty feet!""
Just the entire way the Weasleys are so matter-of-fact about the de-Gnoming. Harry is shocked at the process (yank an incredibly ugly creature out of the bushes, spin them over your head to get them good and dizzy, and fling them far enough away that they can't find their way back), and to the Weasley kids, it's just like weeding the yard.
The Weasleys and Harry watching the gnomes stagger off, while one of them comments that they'll just show up again because they love living there. Bonus for the casual mention later that when Harry glances out of Ron's bedroom window at the end of the chapter, the gnomes are already filing back into the yard.
After Snape fails to get Harry and Ron expelled, he's described as looking "as though Christmas had been canceled."
Becomes Actor Allusion when one remembers Alan Rickman's earlier turn as the Sheriff of Nottingham:
"Cancel the kitchen scraps for the widows and orphans, no more merciful beheadings...and CALL OFF CHRISTMAS!"
Harry: Hang on, there's an empty chair at the staff table. Where's Snape? Ron: Maybe he's ill! Harry: Maybe he left, because he missed out on the Defence Against the Dark Arts job again! Ron: Or he might have been sacked! I mean, everyone hates him— Snape:(from behind them) Or maybe he's waiting to hear why you two didn't arrive on the school train.
[Referring to getting Moste Potente Potions via telling a teacher they're "just interested in the theory" of Polyjuice Potion)] "Oh, come on, no teacher's gonna fall for that!" said Ron, "they'd have to be really thick..." [end chapter] [start of next chapter] Since the disastrous episode with the pixies, Professor Lockhart had not brought live creatures to class...
I can't remember if it was stated in the book, but where did the basilisk come from?
Salazar Slytherin hatched it a thousand years ago. It's been waiting all this time for the Heir of Slytherin to come and say "Wanna play fetch? Go get the mudblood! Go get it! Good giant snake thing! Atta boy!" note It's actually a girl.
Incidentally, when Harry is tricked into thinking Hagrid opened the Chamber of Secrets, he imagines the young Hagrid trying to fit a leash on the Beast.
"Everybody line up! Harry Potter's giving out signed photos!"
Hagrid upon hearing this: "I've heard you've bin givin' out signed photos. How come I haven't got one?"
When Ron grabs Hermione's timetable out of her hands and says, "Why have you outlined all Lockhart's lessons in little hearts?!"
Also when Madame Pince tries to take the slip with Lockhart's signature on it away from Hermione and she asks, "I was wondering if I could keep it?" and Ron says, "We'll get you another autograph. Lockhart will sign anything if it stands still long enough."
And later on we find Hermione has been sent a Get Well card from Lockhart. Ron's response is "Why do you sleep with this under your pillow?"
"His eyes are as green as a fresh pickled toad..."
At one point, Harry's wandering the school and overhears a bit of a Transfiguration Class, where a student is being yelled at for accidentally turning his friend into a badger. Not long after, the kid shows up, still with black and white striped hair.
At the very end, Ginny reveals that Percy's odd behavior that year was due to his having a secret girlfriend. When she asks the others not to tease him about it:
"Wouldn't dream of it," said Fred, who looked as though his birthday had come early."
Harry, eavesdropping on a group of Hufflepuffs in the library, hides from them... in the Invisibility section.
Harry's constant dodging of Lockhart, who tries to use Harry as a way to get even more famous. At one point, Ron speculates that if Colin Creevy and Ginny ever hooked up, they'd probably make a Harry Potter Fanclub. Harry asks him to shut up, since "the last thing he wanted was for Lockhart to hear the words 'Harry Potter Fanclub'".
Harry's introduction to Fawkes: he's alone in Dumbledore's office examining this bird, who looks old and sickly. Since he's been having people blaming him for the attacks on the students, he mutters that the only thing missing is that the bird dies while he's alone with him, only for it to suddenly bursts into flames and crumbles into ash. Harry is mortified, especially as Dumbledore walks in right afterward, and stammers that this wasn't his fault, the bird just caught fire, etc... Dumbledore's response? "Oh, it's about time! He's been looking dreadful for days, and I've told him to get on with it!" Harry is hilariously bewildered at this reaction until Dumbledore explains that the bird in question is a phoenix.
Dudley teasing Harry by singing "I know what day it is" over and over, only to have Harry retort with "So, you've finally learned the days of the week?"
Dobby's antics ending ruining the punch line for Uncle Vernon's "Japanese golfer joke". While funny on its own, knowing the what the actual joke is makes it even funnier.
When the trio learns that Tom Riddle got a Special Services to the School trophy Ron jokes that he probably got it for killing Moaning Myrtle. Turns out he was half correct.
When Myrtle is lamenting that someone threw a book in the toilet she was in, Ron mentions that it couldn't have hurt her. Cue Myrtle sarcastically yelling "Oh sure, let's throw things at Myrtle because she can't feel them! 10 points if it goes through her stomach! 20 points if it goes through her face!"
Later on, when analyzing said book the only thing they can figure out is that it belongs to Tom Riddle, because it's blank otherwise. Ron says that Tom simply got a diary and forgot to write in it. Then adds "50 points if you hit Myrtle in the nose."
From the film:
RONALD WEASLEY! HOW DARE YOU STEAL THAT CAR!
When Ron breaks his wand when the flying Ford Anglia lands in the Whomping Willow:
Ron: My wand... look at my wand...
Harry: Be thankful it's not your neck...
(cue Whomping Willow ramming the car)
"Where's Hermione when you need her?!"
Funniest line in the Harry Potter movies that wasn't in the books: After Harry and Ron are sent into the Forbidden Forest to "follow the spiders", Ron, who had a previously established fear of spiders, quips "Why spiders? Why couldn't it be 'follow the butterflies'?"
Made even funnier by the director taking advantage of Rupert Grint's voice change hitting mid-movie. Yeah, that voice-cracking wasn't completely intentional.
Earlier in the movie where the duo encounter the Whomping Willow, Ron's line "What's happening?" is so damn funny that watching that scene blindfolded will make you think that Ron is a whining dog.
When Mr. Weasley sits down for breakfast after arriving home, he stares at Harry for a moment - possibly wondering when they acquired another kid - before asking who he is.
Or as Tumblr put it. "Oh crap. Did we have another one? Wait no. This one has black hair. Wait Molly was talking about adoption awhile ago. Did we adopt one and I forgot!?"
When Mrs. Weasley tells Mr. Weasley about how Ron, Fred and George stole the flying car to rescue Harry from the Dursley's:
Mr.Weasley: Did you really? How'd it go? (nudged by outraged Mrs. Weasley, while everyone else laughs) Err, I mean, that was very wrong of you indeed, boys, very wrong of you.
Meanwhile, Harry is trying very hard not to laugh.
The Duelling Club. Lockhart being sent flying as Snape uses Expelliarmus on him and Lockhart's Blatant Lies about how he could have easily blocked it and then tries to get Harry and Ron up to be taught how to block spells, prompting the following line.
Snape: Weasley's wand causes devastation with the simplest spells. We'd be sending Potter to the Hospital Wing in a match box.
This becomes brilliant once you get to the end of the series. After all, Snape had promised to keep Harry alive to honor Lily's memory. He couldn't well let the kid get blown to bits in an unfortunate dueling accident.
Exchange between Malfoy and Harry posing as Goyle: "Why are you wearing glasses?" "Uh... reading." "Reading? (Beat) I didn't know you could read."
Topped off by the look on Tom Felton's face, like the thought of Goyle being able to read is incredibly impressive. (Which, given how stupid he apparently is, is pretty likely)
Especially since it was later stated that Tom Felton ad-libbed the line...aged what, 11? Awesome. Also, right after that line, he made an expression that seems to say "Damn, never thought it'd sound good." and looks incidentally similar with "Not Bad" Rage Face.
The Howler is even more hilarious in the movie than in the book. It actually stops shouting to compliment Ginny on getting into Gryffindor, turns itself into a face to speak, blows a raspberry at Ron, then tears itself to pieces. And the expression on Rupert Grint's face is hysterical.
To top it off, Hedwig's the one that notices the train first, and gets as close to a live-action Eye Pop as possible. (Owls have a special talent that way.)
After Ron uses Floo Powder to transport to Diagon Alley, Mrs. Weasley urges Harry to go next, Harry looking outright horrified at what just transpired.
Soon after, Harry says "Diagonally" instead of Diagon Alley, in which both Mr. and Mrs. Weasley wonder what Harry just said. Also a bit of a Meta-joke as this is how Rowling originally got the Punny Name in the first place.
Malfoy taking a terrible spill toward the end of the Quidditch match. While all of the surrounding extras and professors are genuinely concerned for him, but Lucius can't manage to hide his obvious disappointment. Maybe it's unintentional, but Jason Issacs' grimace during that scene looked less like "hope my kid's okay," and more like "Dammit, Draco, you're embarrassing us..."
After Hermione blows up the rogue bludger that broke Harry's arm, Lockhart tries to heal Harry's arm, much to the latter's horror. Lockhart ends up making Harry's arm stretchy and rubbery to the disgust of the crowd surrounding him.
Lockhart: Ah, yes, well... that can sometimes happen. But the point is... (bends Harry's wrist completely backwards) You can no longer feel any pain. And, very clearly, the bones are not broken.
Hagrid: Broken?! There's no bones left!
Lockhart: ... Much more flexible, though.
Seconds before this, the Bludger tries to take out Harry while he's on the ground, and the last time before Hermione gets there ends up nearly mashing Harry's bludgers.
After the outright disastrous Quidditch match, we cut to the infirmary where Malfoy is groaning like he's in pain, while Madame Pomfrey dismisses Malfoy and tends to Harry with a bottle of Skele-Gro. Harry spits out the Skele-Gro only after one sip.
Pomfrey: Well what'd you expect? Pumpkin juice?
After Malfoy calls Hermione a mudblood, Ron is just about to curse Malfoy, but it backfires terribly due to the former's broken wand. Ron then starts barfing up slugs, while Colin Creevey is trying to get pictures.
While Harry and Ron are using the Ford Anglia to get to Hogwarts after missing the train, Harry falls out of the car and is hanging on to the rear grips for dear life. As Ron tries to grab Harry's hand, the latter finds it hard to due to the former's hand being sweaty.
Harry and Ron being ejected from the Ford Anglia after a terrible run in with the Whomping Willow.
Neville faints during Herbology after hearing the Mandrake's cries. Madame Sprout grumbles about how Neville neglected his earmuffs while Seamus tells her that he just fainted, much to Sprout's indifference.
While Malfoy is holding his Mandrake, he put his finger up to its mouth, and the Mandrake starts biting on it. Malfoy then struggles his finger out its mouth while he glares at the little thing.
Just as Harry and Ron are about to head to Platform 9 3/4, they suddenly crash into the wall, creating an awful little spill.
After Harry and Ron survive the ordeal with Aragog and are left by the Ford Anglia once again, we get this from Ron:
Ron: Follow the spiders. Follow the spiders! If Hagrid ever gets out of Azkaban, I'll kill him!
Also, besides the fact that the car appears to have some level of sentience at this point, the way the car just drives off into the forest can also be funny, because it makes it seem like it lives there now. The forbidden forest is home to giant spiders, centaurs, and a sentient car.
The "Care of magical creatures illustrations - forbidden forest"  on the pottermore website, amusingly has the Ford Anglia as the last thing on the list of the forest's "notorious residents".
The title of Lockhart's book published after the events of the movie, revealed at the very end; Who Am I? Given his fate, it's both an appropriate title, as well as probably the only book of his with any truth in it.
During the part where Lockhart unleashes the pixies, a group of pixies hang Neville from a chandelier. Once Hermione freezes the pixies, Neville lampshades his Butt Monkey status:
"Why is it always me?"
At the standing ovation after Hagrid's return at the end, Crabbe starts clapping along with the rest of the students, only for Malfoy to pull him down by the tie with a "we aren't supposed to clap, dumbass" look.
Uncle Vernon falling out the window when trying to stop Harry from leaving with the Weasleys. The whole scene is a huge Crowning Moment of Funny.
As Hagrid enters the Great Hall after his release from Azkaban, he apologises for being late. The reason? Some 'ruddy bird called Errol' delivered his release papers too late after getting lost and confused. The look on Ron's face is priceless.
The aforementioned Howler scene just wouldn't have been quite the same if it weren't for Errol showing up with it and faceplanting into a bowl of cereal.
Ron: "Bloody bird's a menace!"
Unintentionally funny, to be sure, but Lucius Malfoy's attempted Disproportionate Retribution near the end of the movie. When Harry tricks him into freeing Dobby - right outside of Dumbledore's office - Lucius whips out his wand and says "Avada-" right before Dobby intervenes. Particularly hilarious because it was ad-libbed: Jason Isaacs admitted later that he literally said the first curse that came to mind. The Killing Curse.
Ron attempting to turn Scabbers, Peter Pettigrew himself, into a water goblet.
Molly reprimanding the boys for busting Harry out is even funnier than in the book. Precisely because she takes breaks in between yelling to say "Harry, how wonderful to see you." Harry looks as if he doesn't know whether to laugh or not at this.
Ginny's introduction (although she's easily spotted at Molly's side in the first film.) The first exchange between her and Molly about her jumper (sweater) is funny in itself, because Molly's rather casual delivery of "Yes, dear, it was on the cat," suggests that finding articles of clothing on pets isn't unusual in the Weasley household. Also, it may suggest that either Ginny or one of the boys (as a prank) put it there on purpose. But then she catches sight of Harry, and the resulting Eye Take is glorious. It's the perfect expression for "11-year-old girl who ran down stairs wearing a nightrobe only to find out that her celebrity crush is in the kitchen, eating breakfast at their table."
Becomes a Brick Joke in the Floo Powder scene. If you look on the mantle above the fireplace, there's a hook in the shape of an orange cat. Presumably this is where Ginny's jumper was hanging.
Pair this, also, with the sheer absurdity of a man roughly the size of a telephone box being able to sneak up anybody.
Colin Creevy tries to get picture of Harry and Malfoy during the Quidditch match as they're flying straight at him. Cue one heck of an Oh, Crap! face as Colin decides he'd best get the heck out of the way.
Oliver gives the Gryffindors a pep talk before their match against Hufflepuff:
Oliver: We play our game, Hufflepuff doesn't stand a chance. We're stronger, quicker and smarter. George: And not to mention they're dead scared that Harry'll petrify them if they fly anywhere near him. Wood: Well, that too.