Factual error: When Mina is with Dracula within Dr. Seward's room, she is wearing a white nightgown through which, at times, you can see her tiny underwear (more visible when he confesses to be Dracula and she is upset about him having killed Lucy - turning her into a vampire), in a fashion that would not be likely to be worn by women in the late 19th century.
Audio problem: When Dracula and Mina first meet on the street they begin to speak. Dracula's voice has not been dubbed during the first sentence or two. Then in mid stream his voice changes from a high pitched regular rehearsal voice to the heavily accented Romanian voice used throughout the rest of the picture.
Continuity mistake: When Van Helsing breaks the news to Quincey after reading the "Vampyr" book, as he says, "Yes, we may still save her precious soul", he's gripping Quincey's coat, and Quincey's left arm is down, but in the previous shot, Van Helsing's arms were down by his side, and Quincey was holding onto the hat on his head. His other arm changes position as well.
Visible crew/equipment: In the scene where Lucy is done in by Dracula in wolf form, as she dies, blood is exploded into the room by "supernatural" forces. If you look in the torrent of blood, you will see the gas, I assume carbon dioxide, from the special effect cannon appear and evaporate.
Continuity mistake: When Dracula helps Jonathan shave, one side of the crucifix around Jonathan's neck is under his shirt. When Dracula sees the reflection of the crucifix in the blade, the entire crucifix is visible, also when we see it's reflection in his eye. In the next shot, it's partly tucked under Jonathan's shirt again.
Continuity mistake: When Jonathan is dining in the castle, as Dracula says "That relationship was not entirely successful", there is nothing on Jonathan's fork, but in the next shot, there's a piece of food on it. The food stays there during the next few shots, until Dracula says "It is no laughing matter", and the fork is suddenly empty again.