During "Heigh Ho", the dwarf mine makes some... unusual echoes.
Bashful: In a mine! Echo: In a mine! Sneezy: In a mine! Echo: In a mine! All together: Where a million diamonds... Echo: Shine!
The scene where Sneezy sneezes underneath the coat he and Dopey were wearing (which results in the coat briefly inflating to twice its original size and Dopey flying out from the top onto one of the beams near the ceiling), was hilarious enough in one's childhood that rewinding and rewatching fifty times in one session was highly necessary.
When Dopey diligently locks the mine vault, then hangs the key neatly on its peg. Which is next to the door. Which renders the entire procedure meaningless, but Dopey is so innocent you don't hold it against him. It's still funny, though.
There's a very darkly humorous scene after the Queen becomes the Hag. She walks down through the dungeon and comes across a skeleton reaching for a bucket of water. Her response? "You thirsty? Here, HAVE A DRINK!" *kicks bucket*
The birds making a loud screech to scare the dwarfs.
Snow White imitating Grumpy when she first meets him.
Snow White: Oh... [crosses arms and deepens voice] you must be Grumpy.
All of Grumpy's lines before he starts to grow fond of Snow White. All of them. He's just so hilariously against her while all the other dwarfs are fawning all over her as if she's a goddess.
Grumpy: Angel, ha! She's a female! An' all females is poison! They're full o' them "wicked wiles". Bashful: ...What are "wicked wiles"? Grumpy: I don't know. But I'm ag'in 'em.
Dopey in his sleep.
Dopey with the soap; it constantly slips out of his hands until, after charging towards it, he swallows it by mistake. Despite the fact that he immediately starts to hiccup out bubbles, he doesn't realize where the soap was until about ten seconds later, and after a slight pause, he goes into a hiccuping frenzy that lasts for the rest of the hand washing scene.
The reason he needs the soap is to wash Grumpy. But the dwarfs are already washing Grumpy with two bars of soap. One gets the idea that the dwarfs just have soap bars lying around, and they tell Dopey to get one when they want him out of the way.
The whole washing sequence, starting with the dwarfs surrounding Grumpy with Not So Innocent Whistling and ending when Snow's call to supper makes them drop Grumpy unceremoniously into the tub.
Sneezy yodeling with Dopey bobbing his head with his Adam's apple.
Snow White's first entrance in the dwarf's cottage.
Snow White: Oh!! [the animals run away in fear] What a cute little chair.
Grumpy sticking his tongue out at Snow White.
"NOW I'LL BE FAIREST IN THE LAND!!!" Why is this funny? The Queen yells this while still in her Old Hag disguise.
When the dwarfs return from the mine, Dopey is the last one in the house and slams the door shut.
Other Dwarfs: Shh!
Dopey: [while pointing at the door] Shh!
A behind the scenes example: one animator was animating Snow White lying on her bier while her friends mourned her, while Fred Spencer was animating the dancing sequence; both done to music to set the mood. Cue them both yelling at each other "Cut the sad stuff!" and "Stop dancing in there!"
This bit during "The Silly Song": Bashful steps up to sing his verse only to stop because he's embarrassed. Annoyed, Grumpy starts playing the verse over again, only to have Bashful stop and hide his face in his beard. Grumpy then angrily slams all the keys down on the organ, as if to say "Get on with it!". The rest of the dwarfs find it hilarious.
In a creepy (yet still funny) way, the vultures. Either the witch dies and they get to nom her body... or the Dwarves die and they get to nom their bodies. Whatever the outcome, you can see them thinking "This is gonna be a good night".
The dwarfs wondering what do do when Snow White orders them to wash up.
Snow White admonishes the chipmunks not to simply sweep the dust under a rug. So they sweep it into a mousehole instead. Cue the mouse shoving it out again in a rush, making the chipmunks scatter in surprise and fear.
All the dwarfs realize that the intruder is up in their bedroom and decide that one of them should "go down and chase it up", er, "up, down". They all begin nodding, before they turn to Dopey, who looks arounduntil he realizes they mean him and tries to run away, only for Grumpy and Happy to grab him. Doc gives him the candle and assures him that they'll be right behind him. When Dopey heads into their bedroom, he's startled by Snow White yawning and stretching underneath the sheets. Dopey freaks out and runs downstairs, bumping into the other dwarfs, causing them all to fall downstairs. The other dwarfs freak out in turn and run out of the house one by one, slamming the door and causing Dopey to run into it.
Grumpy warns everyone upon meeting Snow White that the Queen, due to all her powers, could be in the room right now. Dopey proceeds to look for the Queen under Happy's beard, prompting Happy to bop Dopey indignantly.
Even the huntsman has a funny moment. After he refuses to kill Snow White and falls on his kneews begging for mercy, he starts crying... and uses the princess' very own dress as a handkerchief.