Mary and her fixation on wishing Gary would propose to her after 10 years together. She's so completely dramatic about it.
During the "Man Or A Muppet" number, Gary and Walter sing about being at the crossroads of their lives and about how they need to choose whether they're "men or Muppets." In Gary's reflection, there is a Muppet version of him. In Walter's reflection, the audience expects to see the human version of him played by a live actor, and, apparently, get... Jim Parsons.
The fact that Parsons' role was kept secret until the film's release is pretty impressive.
Watch them when they're ushered out of the song: they all look fairy nonplussed, one of them is drinking something, another starts eating a bag of chips, and another is texting on her phone.
The Barber Shop Quartet scene where Beaker pops up with an axe, and the rest of the Muppets just stare at him awkwardly. The song they're doing is Nirvana's "Smells Like Teen Spirit". That was great, when they hold up towels with the lyrics Beaker's says "MEE MEE MEE MO" on it.
Scooter has an attack of nerves when he has to suddenly MC in Kermit's place. Kermit advises him to do what Kermit does: Imagine the Audience Naked.
Scooter: (stuttering and nervous) Y-y-y-y-YOU'RE ALL NAKED. (cut to shot of the audience in boxers and tank tops) ... Well, almost.
Beauregard has apparently been cleaning one closet of the Muppet Theater the entire time since the show ended, and never realized they all left!
The song "Me Party," mainly because of the restaurant patrons' complete and total obliviousness to Mary's song and dance.
Piggy sings this with a table of talking Muppet food in her dressing room including a lot of pastries. Why is the food there? 1.) Because she's lonely, and 2.) she's a pig!
The ending of "Life's a Happy Song," where, as soon as Gary, Mary, and Walter leave on the bus, the crowd lets out a relieved "They're gone!" and collapses.
Also during this song we get Willie Nelson singing "Life is full of Highs" and a couple of other people singing that "Life is a fillet of fish" to which Walter and Gary can only reply with... "Yes, yes it is".
The second performance has Tex Richman loudly remind everyone that they sang it already. Nobody seems to care.
Walter tells Kermit that he gave people the greatest gift in the world...
Walter: Uh, no, the one after that.
Kermit: Ice cream?
Walter: No, the other one.
Walter:[Excitedly] YES, LAUGHTER! THE THIRD GREATEST GIFT YOU CAN GIVE SOMEONE!
After you watch the telethon, you realize that it's very much exactly like how a regular episode of The Muppet Show would play out, save maybe for Jack Black being tied to a chair and doing nothing but complaining, and the money counter hanging throughout! It takes up nearly the same amount of time as a regular episode in the course of the film too, even though in-universe, it takes up two hours!
When Gary, Mary, and Walter start looking for Kermit:
Mary: How do we find Kermit? Nobody's seen him in years.
(the gang passes a man selling Hot Star Maps in front of Pink's Hot Dogs)
Walter:(gasps) Wait, stop the car! I have an idea.
(cut to the trio eating some chili dogs)
Gary: These are delicious! Great idea, Walter.
According to the commentary, this was the first scene written.
When '80s Robot uses his modem to locate the other Muppets, we get some loud beeping and static, making Kermit, Walter, Gary, and Mary react and cover their ears, with this line from Gary:
"Oh, stop it! In the name of all that's sacred, let it end!"
At the end of the lengthy and highly-choriographed Crowd Song as Gary, Mary and Walter leave for Hollywood, somebody shouts "Finally, they're gone!" and everybody collapses to the ground from exhaustion.