One of the best ways to begin a social analysis of mass culture characters (be it telelvision, film, books, comics, whatever) is to identify standard societal stereotypes in the characters. For instance, is there a nerd or a geek? Not necessarily just an intelligent character but someone who is socially inept, doesn't dress fashionably-- you know the stereotype of a nerd. Is there a dumb blond? A smart woman who is recognized as intelligent and thus not seen as attractive? Is there a jock who gets all the girls?
Stereotypes can be used to hurt people, but they also serve an important function in society. They act as a sort of shorthand that allows us to make sense of something quickly. For instance, we all have a stereotype of a classroom and stereotypes of the roles we play in a classroom as a student, teacher or guest. Because of those stereotypes students are able to enter a new class on the first day and sit in the appropriate seats-- they don't sit at the teacher's desk. So don't be afraid of stereotypes and don't dismiss them as always bad. You can use them to begin a discussion.
With the Muppets, I'd start with Kermit as the leader. He's the down to earth guy who holds the group together. What does that tell us about Kermit? What does he tell us about groups? His group is often pulling apart at the seams and all but out of control-- why? What does that say about the qualities necessary to be a good leader versus the qualities necessary to be a good, likeable person?
Gonzo is the outsider. Whether you choose to define him as an alien or a whatever, he is clearly different from the others. There are lots of monsters, pigs, frogs etc. There is only one Gonzo. What does it mean to be different from everyone around you? What does it mean for the outsider to find acceptance in a group? What does that tell minority kids as they watch? What do we learn from the occasional negative responses to some of Gonzo's more bizarre behaviors? What does Gonzo teach us about tolerance and acceptance and the limits there of?
What does Fozzie have to say about a positive attitude and never giving up on a dream? What does he teach us about loyalty? What does it say that the most loyal and eager member of the group is also portrayed as, well, not the brightest bulb in the socket?
What does it say about women in society that there is only one main character who is female? What does her obsession with looks, clothes and herself teach girls? What does her ability to stand up to the males say? What of the fact that she stands up for herself with a karate chop?
Just take each character and think about them. How would you describe that character? What are their most important traits? What are they most often seen doing? How are they connected to the other characters? Are they there because of family connections? What do they bring to the group (what is their function in Muppet society)? Try writing out how you would describe each character to someone who has never heard of the Muppets. What is the significance of them being puppets? What can they say about society that cannot be said, or cannot be said as easily with human actors? Why? Answer those questions for yourself and you'll have plenty to go on!
Hope that helps.