Although parodying Universal's franchise of 1931-1945 (especially 1939's SON OF FRANKENSTEIN) and adhering to clothing and automobile styles of the period, the musical number "Puttin' on the Ritz" uses the revised lyrics of 1946. This is perhaps an intentional decision, as the original racially insensitive lyrics would have provided unnecessary offense.
When Igor, Inga, and Dr. Frankenstein go to catch the monster for the first time, they try to inject him with a sedative. Before she injects him, she squirts a little out the top to make sure no air is in the needle, but when she sticks him with the needle, she does not inject anything. In fact, when she pulls the needle back out, she squirts more sedative onto the ground.
When Gerhard Falkstein meets Dr. Frankenstein in his class, he refers to Baron von Frankenstein as his great-grandfather, while the rest of the film refers to him as the grandfather. However, it is stated later in the film (most notably in the deleted sequence "The Reading Of The Will") that the Frankenstein who's will is being read is the Great-Grandfather, and the infamous Victor Frankenstein is his son, or Fredrick's Grandfather.
In the scene where they are removing the casket from the ground, they appear under the casket to lift it out. That would be impossible to do unless they dug a huge hole with a way to get under the casket.
When Fredrick and Inga are caught after having sex, the shot of the platform coming down from the roof is reused from when the monster is reanimated. you can see Dr Frankenstein's legs and lab coat standing on the side of the platform as it lowers.
In the 'Puttin' on the Ritz' number one of the electric footlights explodes, alarming the monster. The light however stays entire and is still on, and it isn't clear what it is that Gene Wilder is stamping out.