In Nice to Have Gnome You, Miss Piggy asks Nanny what would happen if someone lost a library book and what the library would do to that person. At the time, Nanny was watching a cooking show and we get this response:
Show Host: Well first we chop off their little heads!
When the kids are imagining themselves in a maze and find a port hole that opens to... underwater:
Fozzie: Gee, I didn't know water could stand up on its side, Kermit.
The climax of "The Next Generation" hilariously invokes the show's various sci-fi spoofs - Star Trek, Star Wars, The Jetsons - by having different sets of parody characters show up in the same time and place via time travel. This results in several Kermits, Piggies, and so on interacting with each other on top of the episode's Running Gag (the unstoppable Ear Worm of the Jetsons parody theme song).
Piggy:(after the fourth Kermit character appears) I don't know who's writing this, but give 'em a big bonus!
"Kermit Kristofferson's" attempt at writing a country song for "Piggy Parton":
Hoome, home in the swaaaamp
Where mosquitoes and fireflies rooomp
Where, if you're a toad,
Better stay off the road
Cuz the cars that go by, they don't hooonk!
*cue car screech sound effect, a loud ribbit, and Kermit wincing*
The end of "Beauty and the Shnoz" has Gonzo trying to woo Piggy with the help of Cyrano de Bergerac and C.D. Bales, along with everyone else yelling advice at him from the audience. It gets so crazy that Gonzo ends up mixing them up, and saying completely off-the-wall things like "your eyes are like chickens and your voice is a tinkling computer!"
In one of the "Go bye-bye!" bumpers, Gonzo was standing on top of Old Faithful, which is starting to erupt. Then we cut to a live-action shot of it erupting along with Gonzo screaming.
When the kids send in 25 boxtops to get the prize, they wonder what the company wants with all those old box tops, and Fozzie rants for a long time at Motor Mouth speed about how they probably have a bunch of boxes without tops that they need to collect box tops for so they can sell them so the kids who buy them can send them in so they can out them on even more boxes... When he finally stops, a completely floored Kermit just turns to stare blankly at the camera.
Kermit: You know, it sounds scary, but I think I almost understood that.
In one episode, the kids were making paper airplanes, Fozzie's all crumbled up. He tries to fly it, then shows a live-action footage of an old bi-plane falling down, then we hear the sound of a splash. We see it landed on Miss Piggy's cup of milk.
Miss Piggy: Fozzie, what is your plane doing in my milk? Fozzie: Diving for cookies? [Piggy squeezes the milk out of the plane on Fozzie.]