When Beauchamp is attacked by the mummy, he fires 7 shots from a 6 shot revolver.
Obviously the actor playing the mummy is not really missing his hand, but the fake stump could have been much more convincing had he not prominently bent it at the wrist to aid in carrying things.
The drum shown during the sarcophagus opening is from the early 60's.
During one of the 19the century scenes, there is a modern lit exit sign visible over a doorway. Those exit signs had not been invented yet.
At the public showing of the mummy, the audience was shown a film about finding the tomb and contents. The film was in full color, a process that had not been perfected in 1900, when the film was set.
Similar to the movies Land of the Pharaohs and Noah, a knife is used that seems to predate the Bronze Age, never mind the Iron Age.
The mummy should not have been able to respond to an incantation or instructions spoken in 20th c. English.
The film is set in 1900 but Jeanne Roland's hairstyles and evening dresses are all from the 1960's.