Revealing mistake: When Alex uses his time machine for the last time to destroy the Morlocks, watch the closeup of his machine when it's activated. In the lower left hand side of the machine you'll see Alex's laboratory in the background. This is confirmed by director Simon Wells himself in the DVD commentary.
Revealing mistake: During Alexander's long journey, it shows an elaborate geological sequence. It shows the area turning to desert and then trees and plants begin to grow. If you look at the background, trees grow up, then shrink in the same manner instead of dying and falling over. The special effects crew just reversed the growing sequence.
Revealing mistake: When Alexander is about to wake up at the end of his journey from 2037 to 802,701, it cuts to a shot of the year display counter on his machine. The 100,000's digit is spinning just as fast as the 1's digit and all the others, rolling over several times without the millions digit moving. If the counter was moving correctly, as it is in all other shots of it, then the 100,000's digit should be moving slowly, or the millions digit should also be moving.
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.