In the opening scene at Newgate Prison, the excess end of the rope for the noose changes length from long, to cut off, to long again between shots.
Rankin leaves the dance hall and visits Burk to try and get authorization to exhume Styles' corpse. Denied, he visits Westgate prison and after a failed argument with the warden, he faints and is placed in a cell for an indeterminate period of time before he heads home for some familial interaction. After that, he's off to the prison cemetery where he digs up the corpse. Finally, he again enters the dance hall where the same people are sitting in the front row.
One scene shows an evidence box from the Jack the Ripper case but the Haymarket Strangler that starts the movie took place in 1860 and the rest of the movie is 20 years later (1880). The Ripper killings were in 1888, eight years after the movie takes place.
When Karloff's character places his lantern on top of the gravestone it can be seen to contain an electric light bulb.
In the graveyard scene, the bones of Edward Styles are displayed so that his hip bones are placed up by his shoulders, perhaps indicating scapula.
During Karloff's final transformation, he is in a cell, in bed. The camera picks up white above his gum---no doubt, the cotton stuffed under his upper lip.
In his cell Rankin smashes a light globe and then picks up a long piece of glass that could not have come from the round globe.
During the first scene, when they go to hang a man, every extra in the audience is made to look from the previous (19th) century, but the close up on the man they're about to hang reveals a very '50s look: haircut, shirt and all.