When Anna is waiting outside the hotel for her Uncle Buzzy and Carolyn Crossland/Claire Poulee to return the main door can be seen in the background open. But when she decides to enter alone she is then seen opening the door herself. A few minutes later when she is seen looking for personal effects of the ghosts behind the reception desk, the door is open in the background but when she runs from her encounter with the ghosts it's closed then open again in a matter of seconds.
No explanation is ever given for how or where 10-year-old Abigail got hold of a witch's spell book.
Near the end of the movie, when Abigail Gregory professes that "the spell is cast" and the elevator "will crash the way it was suppose too 60 years ago", the mathematics of that statement is incorrect. Since the movie is set both in 1997 and 1939, that is a time gap of 58 years.
In the 1939 flashback scene, such as when the Tower gets hit by lightning, what seems to be the Capitol Records Building can be seen. The Capitol Tower did not exist at the time when Sally Shine died until it was completed in 1956.
In the opening music montage at the Hollywood hotel, you see the band playing and they show a closeup of a man in the band wearing modern seeing glasses.