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.
The only way Dr. Frankenstein could have known about the hanging in advance was if he'd actually met the condemned man on the train to Transylvania (in another deleted sequence that was a spoof on the one from the film "MAD LOVE.") This in turn would mean that Peter Boyle actually first played the convict, Rollo, in the deleted sequence.
Throughout the film, Frederick is referred to as the grandson or great grandson of Victor Frankenstein. However, Victor was a character from 1818 when the novel was first published, which would make Frederick in the 1930's Victor's great-great-great-great grandson, minimum.
The candle that operates the bookcase door appears to go out momentarily, and then comes back on, before Frankenstein and the assistant go down the passageway, but it simply got caught in a draft and dimmed completely down before coming up again - normal behavior of candles.
When the criminal is being hanged, it's raining heavily. When he's buried, the gravediggers are shoveling dry, almost dusty soil onto the grave. When Frederick and Igor dig him up, the mud on their clothes and the coffin is soaking wet and water can be seen dripping down near where Frederick had been lifting. This may have been intentional for Igor's "could be raining" line.
When Gerhard Falkstein meets Dr. Frankenstein in his class, he refers to Baron von Frankenstein as his great-grandfather, whilst in the rest of the film he 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 Frederick's Grandfather.
Throughout the movie, Kemp uses his left hand to move his prosthetic right, but as the villagers are looking for the Monster through foggy forest, Kemp uses his right hand to adjust his left, complete with sound effects. Probably deliberate.
When the policeman confronts the chained-up Creature in the jail, he pulls a cigarette from behind his ear, grabs a match and lights it. He notices the Creature doesn't like fire. When he grabs a second match to scare the Creature, it looks as if his cigarette is inexplicably back behind his ear again. But for a fraction of a second at the very start of the shot, his left hand is actually on the cigarette, putting it there.
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 Frederick is stamping out.
When Frederick 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 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.
As Frau Blucher escorts Inga, Igor, and Frankenstein into the castle, the horses whinny at the mention of her name. Cloris Leachman can be seen putting a hand to her mouth to stifle a laugh as the scene fades to black.