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.
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.
Trivia: It seems like a mistake, but it really isn't: Director Nicholas Meyer, in his DVD audio commentary, points out that the time machine should not have stayed in London and rightfully did belong where it ended up - in a museum in San Francisco. This is plausible not because of alternate dimensions or time zones, he explains, but because the machine was crated up and shipped there by museum curators after H.G. Wells' death/disappearance.