Continuity mistake: In the scene where Inga, Fredrick and Igor throw the net over the monster, Inga sticks the syringe of the sedative in the monster's back but does not push down on the top, yet the monster still falls over. A few seconds later when she collapses on the monster, you can see all of the fluid inside spray out.
Revealing mistake: Right before Doctor Frankenstein (Gene Wilder) gives life to his creation he is standing behind the monster on the platform giving his speech. While he is giving his speech you can see the "dead" monster breathe, not only once but several times.
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.
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.
Continuity mistake: At the castle, Dr. Frankenstein throws darts while talking with Inspector Kemp. The shot of the darts hitting the board does not match with the shot where Inspector Kemp takes the darts back from the board.
Continuity mistake: During his lecture on the brain, Professor Frankenstein draws the medulla oblongata on the black-board twice.