Continuity mistake: When everyone has been turned into animals, Police Cheif Wiggum, as a pig, takes off his tattered shorts and throws them into the fire. Later in the scene he's magically wearing them again.
Continuity mistake: The people standing to the left of the rock, as the Comic Book Guy (as a faun) walks onto it, changes. In the first shot the police officers and Raplh stand there, in the second shot it's a panda.
Audio problem: When Homer is playing the piano, and Marge is playing the cello, Frink grabs Homer and pulls him into the room. However the playing of the piano continues, even after Homer is pulled away.