Shakespeare's plays were popular with all classes during his day, which accounts for his success as a businessman (part owner of his theatre company) and as a writer. It would be hard, I think to say which class was amused by what, rather safer to acknowledge that the humor was enjoyed by all.
That said, Shakespeare did include, even in his tragedies, characters whose job in the play was to "be funny." Certainly Bottom serves the purpose in A Midsummer Night's Dream.
But who was amused by him? Well, first of all, the actors would have been. Bottom lampoons the sort of actor everyone who's worked in the theatre knows -- the diva. He's the actor who wants to tell all the other actors how to play their parts and thinks he could do them all better than anyone else. He's the actor who milks all of his lines and stage time (notice for example, how many times he says that he dies as Pyramus in Act V). So, even today, actors and theatre people everywhere, get this humor.
But he's not only an actor, he's a bumpkin. All of Bottom's fellows come from the working class, and, as such, are ignorant of how exactly to put on a play. Shakespeare makes fun of these simple hard-working fellows, and probably all classes found this funny, even those who saw themselves in the "rude mechanicals." The actors playing these parts would have been adept at these "clown" characters, and audiences probably recognized their favorite actors, who tended to play the same type parts over and over.
As for superstition, it was a part and parcel of 16th century life, so it is also safe to assume that all of Shakespeare's audience was superstitious. Unlike a play like Macbeth, however, Midsummer doesn't really trade in superstition, more the fantasy and magical aspects of the supernatural. By setting all the supernatural events in the forest and casting the dreamlike quality over everything, there isn't anything ominous here to cause alarm in someone who was superstitious.
Lighthearted, magical happenings and poking fun at actors are two aspects of A Midsummer Night's Dream that would have amused audiences in Shakespeare's theater.
i think.. bottom represents the motto "from rags to riches" in a way? he can be relatable to common people --he went from unnoticed to praised (and by the queen of Fairries, -not just anyone) but ofcourse his 15 minutes were up by the next sun which in a way could be relatable to superstitious poeple because they believe good things don't last and well his fortune didn't either. i hope this doesn't confuse you or doesn't sound too lame.