Many younger viewers should recognize the monster, played by Peter Boyle, as Frank Barone.
Lesser-known example: the sadistic jailer who mashes the Monster's Berserk Button one time too many (scaring him with lit matches) is Oscar Beregi, who played the sadistic Nazi who receives a suitably karmic punishment in the Twilight Zone episode "Death's-Head Revisited".
Igor's hump, which changes position from scene to scene; Marty Feldman decided to do this on his own, without telling anybody beforehand. When someone finally noticed, they added a bit where Frederick does as well.
During a search in the forest, Inspector Kemp's wooden arm appears to have switched sides. On closer inspection, it's actually the entire scene that's obviously been flipped as his eyepatch and monocle are on the other eye, and his badge is on the other side.
Brooks ad-libbed the sound of a cat getting hit with one of Frederick's darts.
Almost a Throw It Out moment; in some interviews, Mel Brooks stated that the only point during production where he and co-writer Gene Wilder seriously disagreed was the inclusion of the "Puttin' On the Ritz" number. Gene loved the idea but Mel hated it. After Gene vehemently defended the scene, Mel decided, "If you feel that strongly about it, we'll shoot the scene. If it works, we'll use it, if not, we won't." They shot it and it became one of the highlights of the movie.
The monster's shout of "PUTTINAHNDARIZZZ!" was Peter Boyle's idea.
Wilder wrote in his autobiography that he kept trying to find ways to add additional scenes to the shooting schedule because the cast had a thoroughly great time together and Wilder didn't want filming to end.
The bit where Frederick accidentally stabs himself with a scalpel wasn't in the script—Gene Wilder accidentally did that for real. And kept going.
Continuity Nod: A lot of the laboratory equipment were Kenneth Strickfadens original props from the 1931 Frankenstein.
The Aerosmith song 'Walk This Way' is named after Igor's cane gag.