The part where they take the stairs and Georges rides Edgar piggy back after attaching his cane to Edgar's suspenders and using them to launch himself onto Edgar, shouting, "Upward and onward! WHEE!"
Immediately followed up by "Am I going too fast for you?", while Georges is ON TOP of Edgar.
Edgar's entire reasoning for why he sent the cats away is, in of itself, a hilarious conclusion he made, believing the cats literally have nine lives.
He also starts said equation by multiplying four by twelve (since there are four cats and he muses that they'll live about twelve years after Adelaide's death), as though the cats are living their lives in succession.
This exchange when the three kittens are stuck in the pet door.
Toulouse: Why should you be first?
Marie: Because I am a lady, that's why!
Toulouse: (snickers) You are not a lady.
Berlioz: You're nothing but a sister! (Pulls Marie's tail and bumps her back into the door)
While Berlioz and Marie are fighting, Toulouse pushes a candlestick which lands on Marie's head.
When Berlioz accuses Marie of starting their tiff, she replies with "Ladies do not start fights, but they can finish them." Berlioz replies by sticking his tongue at her.
Toulouse's painting lesson results in an abstract picture of Egdar, whom Berlioz calls "Old Picklepuss". Duchess has to stifle a laugh before she can admonish her kitten.
Berlioz is keen to show off his piano skills, causing Marie to roll her eyes. Then, when she tries to start the next verse, she does a Double Take as Berlioz starts an impromptu piano solo with all four paws on the keys.
Toulouse abandons his painting to join in on the song. He's still covered in paint, though, which means he splashes it everywhere as he hits the keys. Berlioz is not amused, especially when some orange paint splashes in his face, earning Toulouse a Disapproving Look.
The Sibling Rivalry escalates near the song's end when Berlioz and Toulouse get into a piano duel, jumping around on the keys in a bid to end the song first. Getting carried away, they end up colliding in midair and falling onto the keys, ending the song with a discordant note instead.
When Edgar gives Duchess and the kittens the milk laced with sleeping pills:
Edgar: Sleep well! I-I mean eat, eat well, of course!
"Rock-a-bye kitties, bye-bye you go. La-la-la-la, and I'm in the dough..."
When Edgar sneaks out of the house with the cats, he gets "held up" by a tree branch, notices that he's approaching a police station and promptly hauls ass in the opposite direction, only to then accidentally ride down the steps into a subway station.
Also, when Edgar rides his motorcycle up to the point of the dogs chasing him, his hat flips off his head every time the motorcycle backfires... which happens a lot during that time.
This line from Napoleon. Pat Buttram's delivery and timing have to be heard to be believed:
Napoleon: Wait a minute, I'm the leader. I'm the one that says when we go. (Beat) Here we go. Charge!
The way O'Malley stops the milk truck: By leaping onto the hood of the vehicle with the most priceless "psycho-kitty" expression and pose◊ to scare the daylights out of the driver, complete with a comically loud cat screech and the camera shaking. Even funnier when he made another screech while upside down and shaking his head.
When the kittens decide to play "train", Toulouse shouts "Marie's the caboose!" Marie shoots Toulouse an epic Disapproving Look.
Amelia and Abigail spot O'Malley at the river and assume he's trying to learn how to swim. They decide to teach him and almost end up drowning him in the process.
Later when they save him, he refers to them as "Chicks", making them laugh before they correct him that they're geese. He snarks back by saying "No? I thought you were swans!" which earns him a glare from Duchess.
Uncle Waldo.
"Now, girls, don't go shooshing your old Uncle Waldo! Why, you'll wake up the whole neighborhood! WHOOPEEEEEEEEEEEEEEEEE!!!"
He says hello to them by yelling, "Abigail! AMEEEEELIA! My two favorite nooses!"
Thomas:(After getting a whiff of Waldo's breath) "Basted?" He's marinated in it!
As the three geese are leaving, Thomas and Duchess' comments sum up the whole thing.
Thomas: I like Uncle Waldo.
Duchess: Especially when he's "marinated"!
Pretty much anytime the watchdog duo of Napoleon and Lafayette are on-screen. L'il ol' cricket bug, indeed...
For that matter, the entire chase scene with Edgar and the dogs.
When Napoleon pushes up the sidecar beside the motorbike, Lafayette grabs onto the motorbike so he can get Edgar only for the motorbike to veer away so Lafayette is holding onto the edge of the motorbike, grinning nervously at Edgar, who is smiling deviously and looking between the motorbike and the sidecar before stomping on Lafayette's paws. Afterwards, Edgar winds up being the bridge between the motorbike and sidecar, forcing him to run on his hands. Lafayette then rolls up Edgar's pant leg and begins chomping the butler's bare leg repeatedly like a person would with a corn, making him jump in pain. Edgar's goofy smile before he yelps seals it.
Not to mention the fact that as Edgar's making his getaway from Lafayette and Napoleon, he plows through the stone wall of a windmill, and hits it so hard as to move it.
Lafayette accidentally barks to the tune of the mess call instead of the alarm, then jokes that he made a mess of it.
Edgar later returns to the countryside to recover incriminating evidence from the dogs. Hilarity Ensues.
The aforementioned "little old cricket bug" moment is when Napoleon hears Edgar's squeaky shoes, but Lafayette thinks it's only a cricket bug. When Napoleon says that it's shoes, Lafayette replies, "Oh, cricket bugs don't wear shoes!".
When Napoleon's using his Super Senses to describe Edgar's squeaking shoes, Lafayette asks him what color they are. And even better, his guess of Edgar's shoe color is actually true without him realizing:
Napoleon: Well, they're black— (suddenly snapping) Now how would I know that?!
Napoleon's Super Senses get exaggerated when listening for Edgar's retreat.
Napoleon: Sounds like a one-wheeled... Lafayette: A one-wheeled what? Napoleon: You're not gonna believe this, but it's a one-wheeled haystack! (cue Edgar trying to roll away in the sidecar while underneath a haystack)
Then as the dogs watch Edgar escape with his things.
Lafayette: Well, c'est la guerre, Napoleon! I guess you can't win 'em all. (Napoleon hits him on the head) OW! Ooh, ooh, ooh! Criminiddly!
Also, Napoleon calls his umbrella a "bumbershoot".
The above could be Duchess starting to get groggy from the events of the day; no less funny though.
Roquefort getting shot in the gut by a champagne cork.
Roquefort: Oh he got me!
Many of Edgar's moments can be this, which are brilliantly animated by Milt Kahl. Like when he's spitting out the wine when the cats return from his first catnapping.
When O'Malley instructs Roquefort to find his gang of alley cats to help him.
Roquefort: Alley cats?! But I'm a mouse! O'Malley: Look, I'm gonna need help! Roquefort: You mean you want—? O'Malley: MOVE! Just tell 'em O'Malley sent ya, and you won't have a bit of trouble!
When Scat Cat and his gang run off to save O'Malley, Duchess, and the Kittens, Roquefort finds himself chasing after them. They pass a street corner café, and one patron, seeing a pack of anxious cats followed by a mouse, dumps his wine on the street.
Also, the fact that this is a rare instance in which we hear Sterling Holloway, best known for playing rather soft and timid characters, shout.
Edgar, after successfully trapping the cats (including O'Malley) back in the chest, proclaims "You are going to Timbuktu, if it's the last thing I do!". Cue Scat Cat untying a knot holding up a heavy bale of hay which promptly falls onto Edgar's head.
When Madame is taking a picture of the cats:
Madame: Say "cheese"!
Roquefort: Did somebody say cheese? -FLASH-
The end, with everyone of the cast singing "Everybody wants to be a cat", including Napoleon and Lafayette!
Lafayette: Hey Napoleon, that sounds like the end!
Napoleon: Wait a minute, I'm the leader! I'll say when it's the end... (the words "THE END" literally knock him in the head) It's the end.
◊ to scare the daylights out of the driver, complete with a comically loud cat screech and the camera shaking. Even funnier when he made another screech while upside down and shaking his head.
