Factual error: As the machine is traveling through time George becomes aware of "strange sounds" which, when he stops, turn out to be air raid sirens. At the speed at which he was traveling through time, the sirens would have had to operate continuously for several days in order for him to have been able to hear them.
Factual error: The time traveller can hear external sounds in his machine, which means that vibrations outside of his machine's bubble of space can penetrate it. If this were true however, the machine would be destroyed in mid-travel by the shockwave of the nuclear blast.
Factual error: When the machine is in the laboratory racing through time and the sun whizzes across the window, note that the clouds don't move or change formation throughout the entire 'day'. In reality, clouds can change and move dramatically in only minutes.
Factual error: When George starts time traveling in his lab, we see the sun and moon cross his field of view. But then we see stars circling Polaris in the same area. Polaris is nowhere near the path of the sun.