Even though it most likely hints at his own back-story, Tramp's falsetto and the way he was animated when he re-enacts a woman yelling for the dog to be quiet can be pretty narmy.
After Boris talked about Tramp's Achilles' Heel being his weakness for females, Lady later tells Tramp, "As far as I'm concerned, you needn't worry about your old heel." Tramp honestly has no idea what that means.
Tramp: What you need is a log puller... (The beaver continues chewing on the log, ignoring him)I said "a LOG PULLER"!!!!!(voice rumbles)
Lady digging in the garden and accidentally uprooting several tulips. She guiltily props them upright again.
The night the baby is born, Jim Dear is racing up and down the stairs, cheering in his new-dad euphoria. He runs into the doctor, clearly exhausted after being dragged out of bed in the wee hours of the morning and going through the delivery. Jim Dear excitedly shouts "It's a boy! Doctor, it's a boy!" for what is likely the hundredth time. The doctor's response is a wearily deadpan, "Yes... I know."
The scene at Tony's restaurant, with the owner and the head chef fawning over two dogs, is a riot.
Tony: Joe! Butch here says-a he wants-a two spaghetti speciale! Heavy on the meats-a-ball!
Joe: But Tony! Dog's can't-a talk!
Tony (menacingly): HE'S-A TALKIN' TO ME!
Joe: Okay, okay, he's-a talkin' to you! You're the boss! Mama mia...
Tramp setting up a Let's You and Him Fight between an Irish Cop and a mild-mannered professor to provide a distraction so they can sneak into the zoo. He escalates the argument with a well-timed chomp to the policeman's posterior.
Policeman: AAARRRGGGHHH! Pull a knife on me, will ye?