Plot hole: Mrs. Stevens (H.G. Wells' housekeeper) witnessed HG leaving in the time machine. From her point of view (POV) it disappeared right in front of her. Yet the sign at the museum says that the time machine never worked, despite a witness that it did. (00:19:47 - 00:24:14)
Suggested correction: Even though she witnessed the time machine disappearing, there's always the possibility that nobody believed her if she told them what she saw. Telling anyone about the machine vanishing would have people just writing her off.
Also, it is very likely that once he returned to the past, Wells told her not to tell anyone about it.
Plot hole: When Jack The Ripper checks his watch before confronting H.G. Wells and demanding the key, the hands point to 8:50, the ensuing chase to the museum and demise of the Ripper may have used up a half hour or so, yet the time on the wall clock indicates that it is midnight.
Suggested correction: Movie time and real time don't match, so 3 hours has passed without all 3 hours being shown. The fact that the clock now shows midnight is meant to explain this fact without the need for subtitles to reveal the time.
Continuity mistake: When Mary Steenbergen and Malcolm MacDowell are in a restaurant and he's eating ice cream, his hand holding the ice cream spoon is in a different position when he's shown from the front than from when he's shown from the back - one way it's up, the other it's down. Also, the spoon disappears whenever the shot is from the back.
Audio problem: When Wells is en route to the Hyatt, exhaust sound from the taxi as it descends the hills of San Francisco seems to have been stolen from the Mustang in "Bullet." When the taxi pulls up in front of the hotel, it sounds again like the ordinary taxi that pulled away with Wells earlier.