Revealing mistake: In the classroom Frederick stabs himself in the leg with a scalpel. Look closely and you can see the thick pad covering his thigh inside his trouser leg. (00:11:10)
Continuity mistake: During Inspector Kemp's visit at the Frankenstein manor, Frankenstein is playing darts while he is having his conversation with Kemp. He throws the first dart at the bottom 10, but by the time he throws the second dart at 7, the first dart he threw at 10 is now at the bottom of 18. (00:56:20)
Visible crew/equipment: After the monster catapults little Helga from the seesaw to her room and she is tucked into bed, it is possible to see the wire that was used to pull the covers up (when her parents enter the room). (01:06:25)
Continuity mistake: During the scene where the blind man, Gene Hackman, is serving soup to the monster, the blind man spills 2 large ladles of soup onto the monster's lap. The blind man then burns the monster by lighting his thumb, thinking it's a cigar. The monster screams, and breaks through the front door, leaving the blind man's cottage. When the monster leaves the cottage, there is no sign of the spilled soup on his clothes. (01:08:50 - 01:10:55)
Revealing mistake: For most of the opera house stage presentation, the monster is a full head taller than Friedrich. During the tap dance, however, they're the same height. Although the camera angle/depth of field used tries to disguise this by keeping Gene Wilder in the foreground for most of the shots, it's still apparent that Peter Boyle isn't wearing his probably-impossible-to-dance-in platform shoes during the sequence. (01:24:00)
Continuity mistake: When Frau Bluecher is talking to the Monster for the first time, she puts her hand on his head. In a closeup shot of the Monster's face her hand and arm are missing.
Audio problem: When they first find the monster conscious, Frederick says "Is the sedative ready?" The reply, "Yes, doctor," comes from Frau Blucher, who isn't there, and doesn't make another appearance in the film until she releases the monster and he escapes. It should've been either Inga or Igor saying it.
Plot hole: Kemp, after visiting the castle, would've assured the people that Dr. F. Was not making a monster. So, why is that guy boarding up his house if he has no evidence that a monster even exists? Even if he did tell them that he believes that Dr. F. Was creating a monster, how did the guy know that it had escaped? Also, he says that he remembers the last time. He wasn't old enough to remember something that someone else's grandfather did.