Jarrod implies that corrupt French official Jean Paul Marat, when assassinated, was taking an ordinary bath. In fact, Marat was suffering from a tropical skin disease and being in water could ameliorate his suffering, so he spent most of his time in his bathtub.
After inspecting the wax Joan of Arc, Sue tells the police that she thinks it is her dead friend because the figure has only the right ear pierced. It is clear from the earlier scene that Sue only saw the figure's right ear, and could not have seen whether the left ear was pierced.
When the character of Henry Jarrod first appears following the fire that disfigured him, he limps with one foot at an awkward angle but by the end of the picture when he's trying to elude the police he runs up the stairs with the agility of an athlete.
When Sue is running down the street trying to get away from the disfigured man, you can see that her hair has come partly undone in the back, but when she enters the Andrews home only the hair in front is messed up, the rest of her hair is once again up in a bun and neat.
During the majority of the film Prof. Henry Jarrod (Vincent Price) looks normal and the skin of his face moves naturally. Near the end, when Sue Allen (Phyllis Kirk) strikes him in the face the wax mask he is wearing shatters, showing that it is hard and inflexible.
During the fight scene between Henry Jarrod and his ex-business partner Matthew Burke, Burke grabs a flail and hurls it towards the camera. As the flail reaches the top of the screen, the camera shakes vertically for a moment. This is because the handle of the flail hit the top of the camera.
When the original wax museum is on fire, wires can be seen pulling some of the wax figures down. The wire attached to the Joan of Arc figure is particularly evident, pulling it down at the end of the sequence.
It's obvious that the "wax" in the cauldron is actually colored water - it doesn't congeal when it hits cooler surfaces, as real wax would do! Further, wax doesn't contain water and therefore, steam wouldn't rise from the surface. Hot wax doesn't put forth any vapor or the like...until it's overheated and begins to burn & smoke like other oil-based materials.