Continuity mistake: At the very beginning of the movie, the clock on the wall strikes three o'clock. In the next scene, when Philby reminds Alexander of his date with Emma, he tells Alexander that it's close to five.
Other mistake: With how fast Alexander is traveling through time, when the pendant falls out of the time machine, he shouldn't be able to see it fall or hear it hitting the ground.
Factual error: While we can only speculate about the imagined physics that allows the time machine to operate, we see that when Alexander accidentally puts his hand outside the protection of his machine's 'force field' during travel to the future, the fingernails grow by at least five millimetres before he snatches his hand back in pain. This amount of growth indicates that his hand has experienced at least a month while outside the field. Since his blood vessels inside the field would only be supplying a few seconds worth of blood, his hand would be starved of oxygen and therefore dead and well into decomposition by the time he manages to get it back within the field. His only option would be immediate amputation to prevent gangrene in his arm.
Factual error: The motor-carriage that is seen outside the skating rink and later on the street by the flower shop, has current bicycle type tires (metal rims and spokes). Most vehicles of the time had wooden rims and spokes, lined with rubber.
Answer: He was only focused on saving his fiancée, he didn't think of anything else. If he did he would have thought about it.