This film was produced before the Production Code. When it was re-made only 20 years later, as House of Wax (1953), all references to drug use were removed and a character was changed from a junkie to an alcoholic.
The wax figures look like real people because they ARE real people. The original plan was to use actual wax figures, but they melted under the heat of the lights used at the time to film two-strip Technicolor.
To emphasize the similarities between the wax figures and the characters, some names are alike. For example, the suicidal Joan Gale inspires the statue of Joan of Arc. Charlotte, who should have been killed to recreate de figure of Marie Antoinette, was also the real name of the young lady who killed Marat, from the 'Assassination of Marat' depicted in the museum.
Contrary to Technicolor's edict, UA shot a black-and-white version of "Doctor X" and "Mystery of the Wax Museum". At least two scenes in the black-and-white version use different takes than the color one: the scene with Lee Tracy and Mae Busch in the house of prostitution scene and the sequence with Tracy in the skeleton room.
This film certainly reveals its pre-code roots: at 00:22, after Florence (Glenda Farrell) turns out the lights in the police station, amid the other complaints a voice can be heard calling her a, "fresh bitch".