Plot hole: When Elizabeth is interviewing Victoria for the first time, she mentions that Victoria had sent her an application, therefore her name had to have been on it. However, Maggie Evans didn't change her name to Victoria Winters until she was on the train en route to Collinwood for the interview, therefore Elizabeth would have been expecting Maggie Evans, not Victoria Winters.
Factual error: In the scene where Arthur first enters the house and starts going through paperwork, there's a shot of Nathaniel Drablow's death certificate which shows 'body was not recovered' in the box next to his cause of death. Such a thing would not be written on death certificates of the time - that box is reserved for 'Signature, description and residence of informant', a heading which can partially be seen as the camera pans across the certificate. For the death to have been registered, an informant's signature would have to have been there. (00:20:05)
Plot hole: Ruthven is apparently bitter that he has been denied his chance of becoming an immortal vampire after Clara steals the map from him, which is why he attacks Eleanor. But why doesn't he just go to the island anyway? You don't need to be invited - Clara, Eleanor and Frank aren't. Having been there once, it seems highly unlikely he can't find it again - he's a naval captain, so navigation and observation are major professional skills for him. And it isn't hidden or magically protected - the local boatmen know where it is and are prepared to take people there, although they won't set foot on it themselves. He could quite easily have gone there without the map, entered the shrine and been turned into a vampire if that's what he wanted.
Revealing mistake: When Alex says they should go find the penguins, he says "To home" and Marty, Melman, Gloria and Julien place their hands on top of his hand. In the next shot it shows all of them together. But due to the position of Julien and his arm length, it would have been impossible for Julien to have his hand fully placed on Alex's hand. (00:05:05)
Continuity mistake: Bryan is cornered in an Istanbul alley and engages in fierce hand-to-hand combat with Albanian gangsters. Bryan takes one of the gangsters hostage, holds a gun to the gangster's face and threatens to kill him. Another gangster doesn't even hesitate to shoot Bryan's hostage in the back multiple times, and the guy drops down dead at Bryan's feet. Bryan is frozen on the spot. Camera cuts to another Albanian gangster entering the alley, holding Lenore hostage. Camera cuts to close up of Bryan, who quickly calls his daughter Kim to warn her. Camera cuts back to a full view of the alley, and the dead guy at Bryan's feet has completely vanished.