Plot hole: Stuart establishes that there is only one of you and that when you travel through time you can repeat things, but it will be you and not your double that does it. But, at the end, when the Duke is going up the stairs and the uncle says "Where have you been...", the Duke is wearing the same clothes as the first time. Yet we see that he goes directly from the time portal to his house in the ballroom raiment of the later scene. Where did the old clothes come from?
Factual error: Leopold recognizes the telephone as the "talking telegraph" he saw at a fair "last year" in the scene where Stuart calls home from the hospital. The first public showing of the telephone was at Philadelphia Centennial Exposition which opened in May of 1876. (He is from April of 1876.) That aside, if he saw a talking telegraph in 1875, it would've been quite a feat because inventor Alexander Bell submitted his patent in 1876.
Continuity mistake: In the hospital Stuart tries to grab his neighbor's phone. When he detaches him from his life support and alerts the nurse he holds the receiver in his right hand. The camera changes to a shot from behind, and he picks up the receiver again with his right hand.
Continuity mistake: Toward the end of the movie when Leopold is making his speech of who he is going to marry, there is a shot of the crowd in the room. In the very back there is a person that runs in and stumbles about. Then there is a close-up shot of Kate coming in and stumbling around the exact same way.
Continuity mistake: When Kate is on the top of the roof with Leopold eating dinner, you can see her dress has straps on her shoulders. When the camera shoots back and forth from Kate to Leopold, you can see that the strap has fallen off her shoulder and shows her bra strap. However, when they go back to Kate it is back on her shoulder.
Continuity mistake: Stuart has pictures from the ball at Leopold's that show Kate standing at the back of the room looking in the room. At the end of the movie, you can see the set up for that picture. However, for Stuart to have *taken* that picture, he would have to have been standing on the platform with Leopold to take the picture, but he's not there.