When Dracula appears in the Holmwood's foyer in the middle of the night, there are two coats visible hanging on pegs in the background, one of which is Mina's green fur-trimmed coat which she wore earlier. When Van Helsing and Holmwood enter a short while later, after Dracula's visit, both coats are missing.
When Van Helsing and Mina's husband are pursuing Dracula in their carriage they stop when they find the body of a murdered coachman the audio is mismatched. The sound of the carriage and horses in motion continues even after their coach has come to a complete stop.
At the start of the film, Jonathan Harker's journal narration establishes that it's May. Later, when Van Helsing and Holmwood ask the border official about the date Dracula's hearse would have crossed the frontier (within a week of the events that began the film) the date is given as December 1st.
During the final fight scene when Peter Cushing jumps on the table after pulling away the curtains to let the sunlight in, he knocks over a pile of books that appear to be glued together. However, they are really tied with a cord, frequently done to make a stack of books easier to carry.
About quarter of an hour into the film, immediately following the scene where Dracula attacks Harker and then carries the vampire woman out from the library, there is an establishing shot of the outside of Dracula's castle. It looks motionless, but on closer inspection, a dark figure can be seen rushing past the bushes around the entrance to the castle. The most probable explanation is that it is in fact the top of Dracula's carriage, and the shot was originally filmed for the scene a few minutes later when the carriage rushes past Van Helsing on his first trip to the castle. However, the carriage is so indistinguishable in long-shot, the editors obviously abandoned it and used it here instead.
The door to the Holmwood's cellar has the ability to change appearance. When Van Helsing finds Dracula there, both sides of the door are obviously made of wood with an aged appearance. After Dracula leaves, Van Helsing screams for Arthur to let him out, and after the door is opened, the side facing the inside of the house is green and looks metallic.