Deliberate mistake: The version of Earth that our main characters spend the story trapped in, is one individual second in the past that is identical to Earth in every way, with the only exceptions being there is no life or power. The Langoliers consume all the land in this one second and the remnants fall into a huge abyss. However, if this were like Earth, there should be thousands upon thousands of miles of soil beneath the land, but this is ignored for the sake of the plot.
Suggested correction: It is assumed that the Langoliers ate everything below that point to the Earth's core too.
Deliberate mistake: In one of the scenes where Johnny Depp goes into the bathroom (specifically, when he changes clothes with the other man), Christopher Walken's character looks under the stall. The camera then shows the legs and crotch of a man sitting on the toilet, who still has his boxers fully on, but his pants are down.
Suggested correction: That man was not actually using the toilet. He was posing as Watson (Depp) so that Walken would think he was in the stall the whole time.