Factual error: Otis elevator is called that because Elisha Otis invented the modern elevator in 1859, 17 years before the movie takes place. It had nothing to do with the Duke of Albany.
Continuity mistake: When Kate comes back home after the punctured dinner with J.J., her hair is freshly done. Even if she had ample chance to do this, it's out of the question that the rather messy style she had chosen for the dinner was not intentional on such an important occasion, and there was no reason to change this afterwards. (01:00:25)
Continuity mistake: Leopold tells Kate that by his 30th birthday he had "become a blemish on the family name", meaning he must be at least 30 in 1876, making his birth year at least 1846. When he goes forward in time to 2001, he is said to be at least 148 years old, making his birth year 1853 (2001-148) which would make him 23 years old. (01:11:45)
Continuity mistake: In the close up shot of Kate holding the photos during her acceptance speech, the hand holding the photos is a man's hand. (01:46:32)
Continuity mistake: In the board meeting scene in which the margarine commercial auditions are first being looked at, the video gets paused on the first man auditioning and then the second man auditioning, but in each subsequent shot of the television, it's back to being paused on the first man auditioning. (00:29:49)
Continuity mistake: When Kate appears in 1876 New York, including at the ball, she is wearing a different gown to the dress she was wearing in modern day New York. (01:51:18 - 01:53:10)
Continuity mistake: At the end when Kate arrives at the uncle's house, Otis says "what seems to be the problem?" The doorman looks up at Otis, but the very next shot is Kate and the doorman is looking at her. (01:51:50)