I want to say it was too much focus on new characters (though I do like a lot of the new characters, including many who barely if ever made it past the shows cancellation) and not enough focus on old characters, as well as the lack of full musical numbers. But then again, were casual fans (not us) bothered by those? One explanation for the lack of full musical numbers was that audiences were not interested in musical numbers at the time (I would have liked the full numbers back then, I think I was also expecting an album and maybe a compilation video and kept wondering how it could be done if they cut from so many on-stage acts before they were really done).
Casual fans were probably bothered by Kermit not being the host (and wondering who Clifford was) and might have been bothered by Miss Piggy, Fozzie, and Animal not appearing that often (at the time I really only noticed Fozzie's appearances being limited, I knew Frank Oz was also a director but didn't realize his directorial career limited his Muppet involvement), but would very many of the casual fans have been complaining about not seeing Scooter, Rowlf, Robin, The Swedish Chef, and most of the Electric Mayhem? Not to mention classic characters who were a lot more minor.
Some of the writers and producers have defended their use of new characters, referring to it as a "next generation" of Muppets (maybe it should have been titled "Muppets: The Next Generation"). If "Muppets" wasn't in the title, fans probably wouldn't have reacted so negatively to so many new characters (but then would it have been canceled sooner, if it made it past a pitch or pilot stage?), but with "Muppets" in the title, fans expected to see many of their favorite characters. It is a difficult decision to make in how different from the old show to make it, what expectations to meet or defy. I wonder how the fans would have responded if it was full of old characters, had the same format, but didn't have any of the old recurring sketches (or variants of old recurring sketches).
I think Jim Lewis said in his Muppetzine interview that fans like the old characters because they're familiar with them and wanted to have more of a challenge, which I feel they shouldn't have done. I think somebody else (Kirk Thatcher, perhaps?) said in a Muppet Mindset interview that characters like Lew Zealand and Uncle Deadly are limited (but Lew Zealand has done plenty of non-fish stuff, in fact he didn't use or reference fish in The Great Muppet Caper, the movie where he had the biggest role, and Uncle Deadly doesn't seem like a one-note gag character, not to mention in the years since he has managed to become a major character), but also pointed out that The Muppet Show introduced new characters all the time. But the difference is that with The Muppet Show, there was no real set grouping of what Muppets are THE Muppets (people might have thought of Kermit and Rowlf, and maybe the Sesame Street Muppets, but probably not many others), with TMS locking those Muppets into peoples minds as The Muppets (even if there were occasional further uses of the Muppets name in titles that significantly introduced new characters, like Muppet Sing-Alongs or Muppet Time or the Muppet Workshop toyline). By the time Muppets Tonight came out, fans had higher expectations of which Henson creations are The Muppets (of course, there also seems to be clueless fans who mistakenly refer to the Sesame Street characters as Muppets as if they think the Sesame Street Muppets are The Muppets). The Jim Henson Hour also had a lot more new Muppets than old ones, but I think most people thought of the show as The Jim Henson Hour more than they thought of the first half-hour as MuppeTelevision.
I guess one of the biggest benefits of The Jim Henson Company selling the Muppets to Disney is that they needed to create a distinction in which Muppets are The Muppets, and it seems less likely that a new Muppet show would have so many new characters and very few old ones (though Statler and Waldorf: From the Balcony had several, and The Muppets Kitchen introduced a new character as the lead Muppet, and it seems America's Next Muppet would have brought on some new characters), and we barely got any new Muppet characters on the French Muppet TV or the 2015 series (while it's great we got so many classic characters, I do kinda wish they'd introduced a few more new characters than they did). I remember when the 2002 series was announced (and also when EM.TV announced a series in 2000), I felt confident that Henson would have learned from its "mistake" and not introduce so many new characters at the expense of limiting the classic characters, but I wonder if I am right. Announcements for the 2002 series said that there would be new characters (which kinda worried me about them introducing too many new characters), but the pilot script primarily featured classic characters (I don't remember any new characters in that script). I think the company started to be a lot more aware of the fanbase during the early 2000s, but I can't help but think that if Henson was in charge of the 2015 series, we'd have gotten a lot more new characters and maybe less old ones.
And another thing about Disney and new characters: although they do have Puppet Heap building the puppets now, I can't help but think Disney wants to save money by using whatever puppets are still in working condition. In the last decade we've seen a lot of scarcely-used puppets built around 1996, and I think some of the classic minor characters used in recent productions were the same puppets as before (it was confirmed that they still used the original Lips up until it broke in 2015). I sometimes wonder if the current Bobo and Big Mean Carl puppets are the originals or not (they would have had to have rebuilt Pepe by now - and the Making of Muppets from Space book shows a picture of several identical Pepe puppets being built). The fact that the last two Muppet movies pretty much celebrated their history and that many recent Disney movies have had more nostalgia focus might have played a role as well (and in one of Steve Whitmire's posts, he said that the current head of the Muppets Studio had a "no Muppet left behind" mindset).
It makes me wonder about Sesame Street, if Henson was more interested in creating new characters than Sesame Workshop was, considering we haven't really had many new Sesame Street characters since Henson sold them to SW. I think we did continue to get a number of new characters for about a year after the sale, but those characters didn't really last, so maybe that played a part in it, or maybe it's because the format change happened only a couple years later, making it a bit difficult to really develop a lot of new characters. Though it seems like we've suddenly gotten a lot more new characters in the last few years, ironically after the producer decided to focus on significantly less characters AND the show got shortened to a half-hour (which would mean even less time to devote to characters). Since then we've gotten Julia, Rudy, Rudy's father (not sure how major he is), four new characters from Smart Cookies, Gonker being carried over from The Furchester Hotel to the domestic show (but who knows if he'll continue to be part of the show for much longer?), and the sudden return/recasting of Herry Monster.