Dyeing for Your Art: Boris Karloff removed his partial bridgework to achieve the monster's creepy sunken-cheeked appearance. In Bride of Frankenstein the monster learned to speak, preventing Karloff from repeating the effect; as a result, the monster looks considerably less weird the second time around.
Evolving Credits: Opening credits list all the actors except the one playing the Creature, who is billed only with a question mark. Boris Karloff is only named in the closing credits.
Executive Meddling: The reason that Victor Frankenstein's first name was changed to Henry (which was his best friends first name) was because the producers felt that Victor would sound too unfriendly and severe for Great Depression audiences (but maybe because they made Frankenstein's best friend Henry Clerval a bit of a severe character, they decided to change his name to Victor.)
I Am Not Spock: Boris Karloff subverted this by admitting that the Frankenstein movies are the only reason he became a successful actor.
Playing Against Type: James Whale chose to direct the film because he wanted to do something else than war films.
Bela Lugosi was originally set to play the Monster. He also created his own monster make-up, which is reported to have resembled the eponymous being from the 1920 film The Golem. 20 minutes of test footage was shot with him, but it is considered to be lost. Lugosi got his chance 12 years later in Frankenstein Meets the Wolf Man.
Before this, he was also offered the role of Dr. Frankenstein...which would've made for an especially amusing Casting Gag, as the character's mentor is played by none other than Dr. Van Helsing!
The role of the Monster was also offered to John Carradine, but he refused it because he felt that it was beneath him.