The Muppet Christmas Carol may be to the Muppets what Room Service is to the Marx Brothers. Neither is particularly good, especially in relation to the rest of the Muppet or Marx Brothers movies, but they can still be enjoyed immensely if you are a big enough fan of the Muppets or the Marxes. The films share two significant factors that aided in their surprisingly low quality. Each comedy "troupe" (if you can accept Kermit & Co. as a troupe) had recently suffered from a terrible disruption in their respective commands. Muppet Christmas Carol was the first Muppet movie produced after the death of Jim Henson, while Room Service was the first Marx Bros. movie to be filmed (fully) after the death of producer Irving Thalberg (though, of course, Thalberg was not the Bros.' creator like Henson was the Muppets'). And, most importantly, each is notable for having not been written for their "troupe"; instead the "troupe" was rather ill fittingly dropped into pre-existing stories.
In the case of The Muppet Christmas Carol, that pre-existing story is of course Charles Dicken's A Christmas Carol in Prose, Being a Ghost Story of Christmas (umm, commonly known as simply A Christmas Carol). Unlike previous Muppet vehicles, such as The Muppet Movie and The Muppets Take Manhattan, this one focuses on a main character not played by a Muppet. Instead, Michael Caine portrays the lead, Ebenezer Scrooge, while the old favorites play minor supporting characters from Bob Crachit (Kermit) and his wife (Miss Piggy) to the narrators, Charles Dickens (Gonzo) and Rizzo the Rat (himself). Strangely the Christmas spirits aren't played by any of the star Muppets. In fact, only one of them is even technically a puppet: the Ghost of Christmas Present, which is a burly, redheaded body puppet (has an actor inside) with a Scottish accent.