What makes this actually funny is the Big "NO!" reaction from Utility Belt Buzz is obviously overly dramatic (much likely intentional for Rule of Funny), especially if compared to Luke Skywalker's reaction in Empire Strikes Back. Also, all other Andy's toys except Rex obviously don't bother to pay attention at the battle between Zurg and Utility Belt Buzz seriously.
The ridiculously long list of items Mrs. Potato Head tells Mr. Potato Head to bring with him:
Mrs. Potato Head: And monkey chow!
Mr. Potato Head: Monkey chow? For what?
Mrs. Potato Head: Well for the monkeys of course! Come on monkeys!
(monkeys swarm all over Mr. Potato Head)
Mr. Potato Head: That's it! I draw the line at monkeys! Get my agent on the phone!
The various pranks Woody plays on Buzz during the outtakes. Such as the old "ink on the binoculars' rims" trick. Buzz takes the pranks in stride at first, but quickly gets annoyed, making the whole thing even funnier.
"THIS SPACE FOR RENT."
"DARN IT, WOODY!"
What starts off Woddy's pranks is the scene where Buzz is walking through the entire aisle of Buzz Lightyear toys... with Woody in one of the boxes, making the silliest expression ever at him. Even Buzz can't resist laughing. Woody is such a Troll.
Woody turns Prospector's box around to reveal...Prospector talking to twin Barbies.
The fact that he looks at their asses as they walk out just makes this even funnier:
Prospector: So you two are absolutely identical? You know I could probably get you a part in Toy Story 3... (realizing they're filming) Oh, I'm sorry are we back? Well girls, lovely talking with you! Yes any time you'd like some tips on acting I'd be glad to chat with you. Now off you go!
Woody getting his butt stuck in the roll of duct tape.
Jessie pulling on Woody's string...only for it to snap, and for Woody to be sent flying and crashing off screen. The entire "film crew" cracks up laughing.
Jessie: Can that...Can that be part of the movie now? He lost...He lost his string. (breaks down laughing)
"*BURP* Whoo! I don't remember eating that!"
Slinky's bottom half being implied to be a sentient being, with Slinky congratulating it after the cameras stop rolling.
"Look, Barbie! An big ugly man doll! Oooh he needs a makeover!"
"She's an artist!"
"I'm packing you an extra pair of shoes, and your ANGRY eyes, just in case!"
Toy!Stinky Pete has a solemn, Tranquil Fury air to him; in stark contrast, Puppet!Stinky Pete is a rambunctious Yosemite Sam-type character. Watch as he comes up in the theme song; you can see Toy!Stinky doing a Face Palm.
Puppet!Stinky Pete: Has anyone seen my pick? (Pick is in his rear)
Buzz and the gang are in Al's Toy Barn, where they stumble upon Tour Guide Barbie. Mr Potato Head immediately begins chanting that he is a "married spud", while Hamm tells him to step aside for the single fellas.