The "Don't you cuss with me" scene with Mr. Fox and Badger snarling at each other. The scene is hilarious enough on its own, but it becomes even funnier when you get the mental image of Bill Murray and George Clooney, two of Hollywood's most beloved and respected actors, in the recording booth making snarling and hissing animal noises at each other.
The delivery of "What the cuss? Where'd this giant fence come from, we had a master plan!"
"Why is he wearing that bandit hat?" "His ears were cold."
When Fox and family escape Boggis, Bunce and Bean trying to dig them out of the tree, Bean calls Petey to rent "one Mighty Max, one Junior Spitfire, and a Longways Tornado 375 Turbo". Smash cut to what those are: three different sized backhoes, with Boggis, Bunce and Bean driving them at high speed and laughing maniacally like kids on a joyride.
"Why did they write this in letter cut-out of old magazines?"
"I don't know, but you did do the same thing."
While Rat's death is otherwise treated with dignity, it's punctuated by his eyes making X signs, like in 2D-animated cartoons/anime how KO'd or dead characters have X'd out eyes.