The Time Machine (2002) - 3 major mistakes

Deliberate "mistake": When Alexander is travelling to the future for the first time, it shows a speedy acceleration of the events around him. However, the planes that are seen flying by are moving at normal speeds, or at least speeds way too slow since they should be moving too fast to even see, since skyscrapers are being built in a matter of seconds.

Factual error: When Alexander makes his first trip into the past, you can see the second hand of the pocket watch turning backward. The hand is jumping second by second. This is a mistake. A quartz watch (battery powered watch of our times) would do it this way, but a mechanical one from 1900 would turn backwards the same way it turns forward: 5 steps per second, which for the untrained eye looks like a smooth movement.

Revealing: 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.