The entire dang movie, really, but here are some specific examples:
The boss at the beginning at the movie takes a glimpse at the photo of him and Kermit's and Fozzie's dad, an odd looking bear-frog hybrid.
The fact that jewels are stolen in the most conspicuous way, with Holiday's necklace stolen right off her neck in public. She even notes worriedly that she feared this would happen!
Miss Piggy thinking that Kermit couldn't get her out of jail...because he had to go to law school.
The exchange is hilarious:
Jailer: Miss Piggy, your lawyer's here.
Miss Piggy: I don't have a laywer.
Jailer: Ah, sure you do! Little green guy.
Miss Piggy: Oh, Kermit! No wonder he didn't visit me...he had to finish law school!
"You can't even sing! Your voice was dubbed!"
The goldfish randomly appearing in Miss Piggy's fantasy sequence.
Gonzo hailing a cab. By throwing himself down into the middle of the street right in front of it.
Kermit: Uh, that's very effective.
Gonzo: Yeah, it's great when it works!
Peter Falk's cameo, wherein he lampoons himself as Columbo, telling Kermit that he can tell his whole story just by looking at him. Kermit humors him, and Falk lays out a story that couldn't be further from the events of the movie, even going as far as to name Kermit's faux-brother-in-law "Bernie." Kermit's reaction is pure deadpan goodness. "You know, it's amazing, but you are 100% wrong. I mean nothing you've said has been right."
The scene where both sides (Nicky and his cohorts, the Muppets) are checking their equipment before moving out. While Nicky's gang have the usual stuff, the Muppets' list is a bit...strange.
Fozzie: Wax lips.
Zoot: ...Man, I just had 'em!
Dr. Teeth: Did you leave 'em in your other pants?
Zoot: I don't have no other pants!
It isn't just strange...they don't actually have any of the things they supposedly need to foil the crooks. "Frisbee?" "Uh...lost." "Whoopie cushion?" "I think it's in the bus." "Peanut butter?" "Animal ate it!" "Saaah-reeee..."
But Lew Zealand remembered the paper towels!
Fozzie and Gonzo excited to be in London.
Fozzie: Yaaaaay! We're finally in London, we made it!
Gonzo: Is that the Eiffel Tower!
Gonzo: (while they're crossing the Thames) What do you call this river?
Fozzie: I think it's called the "English River".
Gonzo: Oh. (beat) I'll take a picture of it! (flash)
Fozzie: Oh, sorry. Did I get my elbow in the shot?
Gonzo: Don't worry. It adds human interest.
Fozzie: (beat) But I'm a bear.
The whole "17 Highbrow Street" scene, from the fact that the address actually exists to John Cleese's completely non-chalant reaction to finding Kermit and Piggy in a closet and recommending a restaurant to them. Although it's really more of a supper club.
Gonzo attempting to pay for dinner... by selling pictures of the diners for ten dollars a pop. Keep in mind that the dinner was in the thousands of dollars. And one of the couples was a cheating husband and his mistress.
Man: No, no pictures.
Gonzo: Aw, but it would be a great memento for you and your wife.
Man: My wife isn't feeling well.
Gonzo: That's too bad, maybe she should be at home.
Man: My wife is at home!
Gonzo:(Stammers incoherently) Yes, next table!
Fozzie starting a chain of blabbing about Kermit's date, and then inviting everyone at the hotel to go along with him.
Kermit: Fozzie, this is all very embarassing!
Fozzie: Don't worry, it won't leave this room.
Newsman: This is a Muppets News Flash! Kermit to date Lady Holiday! Details at eleven.
(Kermit makes a face)
The entire first ten minutes, which take a complete and total wrecking ball to the fourth wall by starting with the Muppets lampooning the opening credits and follows it up with a musical number called "Hey, a Movie!".
Kermit taking one look at the supper club's menu and just about having a heart attack.
Kermit: It's just sort of amusing that the roast beef is the same price as an Oldsmobile.note The car company he refers to has since gone out of business.
This exchange between Lady Holiday and Nicky:
Lady Holiday: I feel as if thieves are breathing down my neck.
Nicky[while breathing down her neck]:Thieves aren't breathing down your neck!
Kermit and Miss Piggy having an in-character argument about why Piggy lied about being Lady Holiday, which devolves into an out-of-character argument about Piggy's overacting. It really has to be seen to be believed.
Kermit, Fozzie and Gonzo arriving in England by being shipped ninth-class (in boxes that resemble jail cells labeled "Frog" "Bear" and "Whatever") and then thrown out the plane into a pond. (Gonzo, of course, loves it.)
Steward: All out for England!
Kermit: Oh goody! The plane is landing!
Steward: The plane? (opens cargo door) No, the plane lands in Italy! You land in England!
Kermit proposes a counter-offensive to prevent Nicky's gang from stealing the Baseball Diamond. He emphasizes the danger, and says, "if anyone wants out, now's the time to say it." Immediately, everybody except Gonzo and Fozzie starts opting out!
The entire scene where the Muppets and villains begin to play an impromptu Baseball game with the Baseball diamond, complete with Louis Kazager doing commentary!
Don't forget Scooter selling popcorn and the rats acting like fans!
Kermit's disguise when trying to get Piggy out of jail. A lawyer named Rosenthal. The fact that the name is repeated in exaggerated fashion is pretty funny "ROSENTHAAAL". When "Rosenthal" & Piggy share a kiss from both sides of the screen for the prison visitation booth, Piggy remarks "...you have mesh-marks on your face" and he does.
After breaking herself out of Prison, she tries to hitch a ride with Peter Ustinov in a garbage truck. He tells he that he can't take passengers...but she drags him out of the truck, tosses him to a pile of garbage, where he meets Oscar The Grouch! After carjacking the truck for her getaway, Piggy does a "Convoy/CB Radio" bit.
Oscar: Hey...what's all the racket?
Ustinov: What're you doing here?
Oscar: A very brief cameo.
Ustinov:(Sadly) Me too.
The very first thing you see is Animal, who makes a noise as a parody of the MGM Lion logo. Then he starts eating the rest of the scenery.