(at around 47 mins) When the Professor is locked in the rec room, the door opens and while he's shooting there is a round handle to open and lock the door, mounted on the door. When he stops firing the gun, the shot cuts to him then back to the door and the round handle is gone. Later, when someone leaves the room it is back again.
(at around 1h 20 mins) When Orlock gets his left hand caught in the door chasing Humvee and Aurora, Humvee manages to close the door by force, severing Orlock's hand. In the next shot, the hand falling to the floor is his right hand.
(at around 3 mins) At the start of the movie, a crew data file for Captain Abraham Van Helsing is shown. It lists that he was in the Special Forces from 2989 to 2997, yet it lists his discharge as being 2992.
The Professor and Abraham are examining the bite marks on 187's neck on the medical table. His eyes turn red and canines sprout from his mouth before he lunges at them. They should have been able to see all of this before he attacked yet they act surprised in the next shot.
Throughout the movie, the "plus sign" the man was holding is referred to as a Crucifix, and later on, we see his quarters are filled with them. However, a true Crucifix has the image of the body of Jesus affixed to it. Otherwise it is simply referred to as a cross.
(at around 21 mins) When the crew first finds the skeleton tied to the chair, Captain Van Helsing says the figure is holding a crucifix. In fact, there would have to be a depiction of Jesus on it to make it a crucifix; what the skeleton is holding is a simple cross.
Religion as a concept no longer exists in this film's future, as the characters don't recognize religious iconography when they see it (like crosses and such), yet they still use vernacular like "Jesus Christ" and "Hell" as profanities.
A wooden stake like object is needed to kill a vampire by stabbing them in the heart, yet Humvee clearly stabbed Mina in the abdomen when he killed her and not the heart.
Boom mic briefly visible in 187's room.
The corpse found on the ship is said to have tied himself to the chair. How he ties both his arms to the chair is not explained.
The crew aims the ship toward the suns so the light can kill the vampires, yet the ship has no known windows or portholes.
Orlock tempts The Professor with an offer to turn him into a vampire to allow him to walk again before a noise distracts him and prompts him to leave. A few scenes later however, The Professor is shown to have been bitten and turned into a vampire, despite the fact that Orlock ran away before he could bite him.
(at around 37 mins) The Professor describes 187's throat wounds as being made by "definitely teeth...incisors." The incisors are the front teeth; the teeth that would correspond to vampire fangs are the canines.