Factual error: In scenes that take place in 1912 on the porch of the hotel you can sometimes see American flags in the background. The flags in the movie have 50 stars. The 50 star flag wasn't adopted until after 1959.
Plot hole: Richard eventually manages to travel back in time by removing all the modern items from his room. But what about the spotlights above his bed?
Continuity mistake: When Reeves signs the guest register at the hotel in 1912, his signature is different from the one that he saw in the register that he found in the attic.
Factual error: When Richard Collier encounters the young Arthur in 1912, Arthur is playing with an inflatable rubber ball. Balls of this style were not made until the 1960s.
Revealing mistake: When Richard first wakes up after travelling through time, he's supposed to be lying on a couch. Yet there is a wall behind him. It's blatantly obvious that it's the same shot from the modern bedroom, and all they did was change the lighting.