Someone living in late-Victorian England would have been used to guns being readily purchased legally, much as in 1979 San Francisco. It was only in 1920 that gun laws in Britain began to be significantly tightened.
During the time travel sequence, the voice-over from King Edward VIII's (Duke of Windsor) abdication speech precedes Franklin D. Roosevelt's "Fear itself" speech. FDR's speech came first (4 March 1933), then Edward both ascended and abdicated in 1936.
Although the Whitechapel Murders occurred in the Autumn of 1888, while the London arc of Time After Time is set in 1893, the script specifically states "the Ripper has returned," so this isn't really an error.
When Wells is in McDonald's and sits down to eat the food he comments: "Pomme frites...fries are pomme frites." However, it is clear Malcolm McDowell says the British term "chips" which is later dubbed to "fries" in post production.
The jeweler states it will take a week to get a check and Wells states he doesn't have a week. Wells has a time machine. It would not be hard for him to go to November 14 or 15, collect the check, cash it, and return to November 7.
In the film, Wells, claimed that his writings on "Free Love" financed the construction of his time machine. In reality, H.G. Wells was only 26 years old in 1893 and he would not yet have been an established, acclaimed, and well paid writer that had a large circle of peers, as depicted in the early scenes at his house. The early 1890s was a struggling period for Wells and he was actually living with his aunt due to being unemployed and having little money of his own. This would be after his short lived stint as a secondary school teacher, his first real professional position after graduating with a Bachelors Degree in 1890. Wells did not get his big break until 1895 with the publication of The Time Machine, only after which he was able to support himself with his writing.
H.G. Wells travels from 1893, when he is explaining his machine he says, "12 years ago a French Engineer harnessed the power of the sun to run a printing press." This would have been 1881, but in fact Monsieur Abel Pifre demonstrated his solar powered printing press on August 6th 1882.
Before John Leslie Stevenson (Jack the Ripper) asks H.G. Wells for the return key for the time machine and attacks him, he locks the door to the Hotel room. A maid knocks on the door and then opens it saying, "Room service." The door should have still been locked.
While Wells and Amy are walking on the street they are passed by two men, one in orange pants and the other in a brown jacket. A minute later, the same two men pass them again as the camera zooms in for a closeup of a newspaper report about a murder.
As Wells learns how a car is driven, the automatic gearbox is labeled P-R-N-D. When he first tries to drive it, he starts in Park, but wrongly revs the engine before moving the lever. This should make the car suddenly Reverse, but it Drives forward.
Amy invites her friend to meet Wells for dinner at her place on a Friday. However, when Wells and Amy fly ahead in the time machine in order to stop Amy's death, the day they advance to is a Saturday. When Jack appears at Amy's apartment and kills the friend, it's a Saturday, not a Friday. Amy even says to Wells her friend arrived for dinner at her place.
Though it makes good drama, it is unnecessary for H.G. Wells to chase Jack the Ripper into the future at all, since he could simply travel back a day or two and prevent Jack from leaving in the first place. - There is no evidence in the film that changing history is that easy or indeed possible. Everything that transpires happens in a linear framework. HG travels in time but at no time changes it. Any attempt to do so might have proved paradoxical.
When H.G. Wells travels through time, the windshield of the time machine cracks. But when the time machine is in the museum the windshield is not cracked. - Not windscreen but glasses which are broken. He replaces them on arrival at museum.
Stevenson claimed that he had to have the key so that he could prevent Wells from following him through time. However, there should have technically been two time machines. The one that Wells and Stevenson use to travel to 1979; the other being the one that is in the museum exhibit, which happened to be the same machine, only dismantled by Wells at some point in his future, as explained in the museum recording. The time machine, when it appeared in the museum would have superimposed itself perfectly over the one that was already there.. Wells, built the machine so he should have been able to repair it and fashion a new key.
When Jack/John takes off H.G. Wells' glasses before hitting him, the camera focus is thrown to show how poor H.G.'s vision is. Although Jack/John's face is badly out of focus the wall and door behind him comes into sharp focus, displaying a possible error by the focus puller - to make this effect obvious; everything should be out of focus. However; this effect could be seen as showing Wells as being long-sighted.