At the start of the movie, David wakes to observe Orion at its zenith. He tells his father that it will not happen again for six years. The zenith is the highest point an object reaches in its path from rising to setting. When Orion is visible at night, it will reach its zenith every night, about four minutes earlier than the previous night. David also mispronounces it as "O-REE-on" rather than the correct "O-RYE-on," but this isn't necessarily an error, as he may have only read it in a book and assumed that was the correct way to say it.
The same shot of a soldier manning a searchlight on a tower beside the side of a building is used in both the scene at the rocket base of the attempt to blow up the rocket, and (three times) in scenes in the field where the Martians landed: this latter use is particularly ridiculous because there is no such building as is seen behind the light tower in that location.
Several shots throughout the film are "flipped", run in reverse, apparently to lengthen some sequences. This includes the military police chase of McLean's car after his attempt on Dr. Wilson's life (the vehicles' steering wheels are clearly on the "right" in the flipped sequences), a reversed shot of the fence and path, and numerous shots underground of the Martians and soldiers running through the tunnels.
After Dr. Blake is knocked unconscious, the drones roll her over to place the mind control device in her neck. As they roll her over, the actress clearly helps them move her.
When the desk sergeant calls Dr. Blake the clock on the wall behind him reads 11:05. Some time later, after Dr. Blake has arrived and is talking to David another brief view of the desk sergeant shows the clock still reading 11:05.
When David and Doctor Blake fall through the ground, the shot of the earth closing up behind them is one of the earlier shots of sand closing further up the path. But when Kelston runs over to the spot where they disappeared, the area is plainly covered with grass and dirt, not sand.
Zips can be clearly seen on the alien's suits.
When the soldiers need to blast a new escape route, the boy knows how to work the heat ray. This seems unlikely since he was never present when it was fired.
As the soldiers are setting explosive charges at the sandpit, Dr. Blake takes David aside to tell him that his mother has been found and is being prepared for surgery. As David turns his head toward the rear, it can be seen that he has the cross-shaped scar at the base of his neck that indicates that he has the Martian device implanted in his brain. Nothing else occurs in the film to explain this.