Other mistake: Before the wolf changes back into Evil Ed you can see the black cables pulling the fake wolf across the carpet.
Other mistake: When Jerry is in the nightclub starring at Amy you can see his reflection in one of the mirror columns of the dance floor. He is a vampire and shouldn't have a reflection. (01:02:51)
Chosen answer: First of all, REM didn't record "Personal Jesus," Depeche Mode did. The song I think you're referring to is Ian Hunter's "Good Man in a Bad Time." The other song Amy and Jerry danced to was Evelyn Champagne King's "Give it Up" which could never be confused with "Personal Jesus." I hope this helps!