The monster's coat and shirt are pulled over his chest for Dr. Waldman to perform a dissection. In the next scene, as the monster is coming down the stairs, having just killed Waldman, we see that he has neatly tucked in his shirt and buttoned his coat, just as any newly-created-from-corpses, tortured, simple-minded monster would do.
Early in the film, Dr Waldman presents two brains in glass jars each bearing two neatly typed labels, one in Latin, the other in English. The good brain reads "CEREBRUM" and "NORMAL BRAIN" while the other reads "DYSFUNCTO CEREBRI" and "ABNORMAL BRAIN." When Fritz breaks into the medical school, the typed NORMAL and ABNORMAL labels have been replaced by larger, hand-printed ones.
In the film's first scene, when Dr. Frankenstein and Fritz begin to dig up the newly-interred corpse, they both shed their jackets. After a dissolve to bridge the passage of time, when they reach the buried casket, a shovel is upright in the unearthed soil behind them with one of the jackets hanging on it as well as a hat. . .but neither man was wearing or carrying a hat when they arrived at the grave.
Baron Frankenstein says that Henry Frankenstein's lab is in "an old abandoned windmill". In fact, it is in a castle or watchtower. According to the DVD commentary, this line of dialogue was from an early version of the script, and was left in the final version by mistake.
When Maria meets the Monster by the lake and talks to him, the close shots of her show some vegetation and the lake in the background. She then takes the Monster by the hand and walks him closer to the edge of the lake. When she next talks to the Monster, the background in the close shot is the same as it was before, as though she has not moved at all.
In the scene where Henry and Elizabeth are sitting by the lake and talking about their upcoming wedding, the long shot that opens the scene shows a dog at Henry's feet, laying on his right side with his head up and looking around. However, in the next shot the dog is asleep and laying on his left side.
According to DVD commentary for this film, director James Whale intended this film to take place in an "alternate universe" and therefore freely mixed 19th Century and 1930s technology, hair fashions, etc.
Right before the Monster's awakening Henry Frankenstein replies to the charge that he is crazy by taunting, "One man crazy, three very sane spectators." But there are four spectators: Victor, Elizabeth, Dr. Waldman and Fritz. Fritz is neither a spectator nor called crazy; he is an assistant.
Right before Fritz climbs the gibbet to cut down the hanged man, supposedly a beam of light from his lantern hits and travels across the "sky" behind him, which is obviously a backdrop. The latter is right, the "light beam" however is a lens flare, which is obvious because it also travels before Frankenstein without being displaced - it's an optical phenomenon and not a practical one.
When Dr Waldman reveals that Fritz stole a criminal brain, Frankenstein is unpleasantly surprised. However, his first attempt to acquire a brain was from a corpse on a gallows, which presumably would also have been that of a criminal.
When Fritz steals the brain from the medical laboratory, it is in a jar very clearly labeled ABNORMAL BRAIN. Dr. Frankenstein should not have been startled to learn from Dr. Waldman that the brain he used was abnormal.
In the scene in the film where the monster is dragging a supposedly unconscious Henry up the stairs inside the windmill, on the final stairway, you can clearly see unconscious Henry walking up the stairs alongside the monster, making it easier for the monster to "carry" him up the stairs.
When Dr. Frankenstein and the Monster are fighting atop the burning windmill in medium shot, both their outlines shimmy, revealing the primitive (yet effective) matte process that put the stormy sky behind them.
When the Monster throws Dr. Frankenstein off the parapet from where they are fighting, you can see through both the Monster, the parapet, and the dummy of Dr. Frankenstein as it heads toward the windmill blades.
The monster is famously made up from parts of other men, and the huge scar on his right wrist suggests this. However, any time Karloff is holding both hands in the same shot they are obviously both his and identical to each other.