The only real "con", aside from many characters not having big parts (Link, Dr. Strangepork, Beauregard, etc), is Sweetums' introduction. It just comes off as odd. It seems his reason for being there is to just introduce another Muppet. They don't clearly introduce his name (Mad Man Mooney just calls him his "Jack", Sweetums says "Jack not name, Jack job" but back when I was younger I couldn't understand the whole line AND he doesn't properly introduce his whole name), it's hard to tell whether his turning a fly into a decimal point was intended or not (well, he did purpsoely kill the fly). And aside from lowering the price there's not really a reason for Kermit to invite him to go to Hollywood with them. The only time he's mentioned by name is right after he bursts through the screen and when Lew Zealand talks to him during the hard-to-understand end credits sequence, and in both instances the name mention isn't that clear (well, Lew calling him Sweetums is more clear in the UK version).
And as a kid I didn't really like the Sweetums scenes. With him chasing the Muppets, running out of the tent and through the screen, and shouting so much (combined with the abuse he suffered at the beginning of The Great Muppet Caper) I actually thought he was a bad guy. In fact, for a long time I used to be able to get myself to watch those scenes without fast forwarding or muting the volume. I would fast forward the beginning of the 1993 VHS promo for the movie because it had Sweetums chasing the car. There was a TV commercial for the VHS rerelease, but I'd always leave the room when it was on just in case it had one of those scenes (I still don't know for sure... I know that particular TV ad showed Kermit inviting him to Hollywood). I wonder if I would have had this problem if he caught up with the Muppets by the time they made it to Hollywood, as opposed to crashing through the screen. But now I can watch those scenes without problem.
It's interesting how Kermit invites each Muppet so soon after meeting them, seemingly without going to their homes to at least pack their bags (though Piggy and Sweetums already had their things packed). Fozzie invites Gonzo and Camilla to join them seemingly seconds after their cars collided, without really knowing him. I don't know if Gonzo was on his way to a job or back to his office, but he seemed eager to join them immediately. It almost sends the message that if you're on a road trip you shoudl invite as many strangers as possible.
And does anybody feel that during "The Magic Store" sequence they should have had more Muppets working on the set, aside from Robin (who's hardly noticable there) and Crazy Harry? It seems like this movie-within-a-movie (within-a-movie?) has ALL of the cast being the entire crew as well (but who's to say all those Muppets who suddenly show up are not part of the crew?). I feel during this sequence they should have shown Gladys and The Swedish Chef doing the catering, Beauregard putting up the sets, some of the full-body monsters putting up the sets, Link reciting lines (it would have been a little funny and perhaps appropriate to have Link dressed as Doc Hopper, as if he was going to portray him), stuff like that.
While I always liked it well I think this was my least-favorite Muppet movie when I was a kid (I think it was because of the Sweetums scenes, as I explained above), though now my equal favorites are this, The Great Muppet Caper and The Muppets (while I like The Muppets Take Manhattan less than I did as a kid).