When the show was on the air I found it odd that they'd include cameos by other celebrities who weren't the guest star (and in season two even gave subplots to celebrities without announcing them as guests... I can't figure out why Don Rickles was announced as a guest alongside Coolio). I asked Jim Lewis about this, and he pointed out that The Muppet Show only had one or two guests an episode because it was made in england (I don't know what to make of that explanation... There are English-based celebrities, though maybe such celebrities are only famous in England but not America... But there have been plenty of things made in England that have become popular in America; I've read that the Superman and Star Wars movies were filmed in a studio near the one The Muppet Show was made at).
I was turned off by the fact that whenever they'd start a musical number they'd rarely show the whole number (are there any episodes where all the songs are presented in full?), but Jim Lewis has explained that at the time, musical numbers weren't as popular with the public (which can explain why Muppets from Space wasn't very musical). I don't mind stuff like Firefly and Steppin' Out with my Baby, where it constantly cuts back-and-fourth between on-stage and backstage. That kind of stuff was a little bit common on The Muppet Show (the closing number from the Jonathan Winters episode is an example, or the gargling number with Mark Hamil and Angus McGonacle... Hmm, when thinking about it, I guess it wasn't that common on TMS after all).
It's been said that the Johnny Fiama Leaves Home episode was the episode where the writers figured out what they were doing, but I don't quite understand what it meant. I watched the episode online last summer... It seems it doesn't focus much on the show, and has quite a bit of scenes outside the studio. But are the scenes at Johnny Fiama's home any different from Beaker's Star Trek cruise, Kermit's date with Gilbert Godfried, Bobo on locaiton looking for a guest star, Piggy's ride to the studio, or the various scenes with Statler and Waldorf watching the show (though with the exception of the last one mentioned, all of them were subplots if not part of the main plot)? Though the episode does have only a handful of sketches (I think this is the only episode produced for season two to feature Bay of Pigswatch), and it seems most of them just come out of nowhere. Last year on the Tough Pigs forum there was a thread about Muppets Tonight, and it was pointed out that this one doesn't have much Clifford while Kermit doesn't appear at all (aside from a monitor image showing the "Once in a Lifetime" number).
I think the people on ToughPigs speculated that most of the writers were more experienced with sitcoms than Muppets, and were really creating their own universe, one where the new characters fit in better than the classic characters. Someone mentioned that Gonzo, Bunsen, Beaker, and Miss Piggy fit in with the format, but Kermit and Fozzie don't (and with the exception of Johnny Fiama Leaves Home and The Best of Muppets Tonight, Kermit appeared in new footage in every episode, even in cases where his pressence seemed forced).