Revealing mistake: After the crew decided (rather arbitrarily) to use fire to scare the monsters off, the camera zooms on Jack. The zoom through the plane window is a digital effect with the plane being all CGI, and it shows because the perspective is all wrong. Jack would have never been visible from the window at that distance and at that angle. (00:55:55)
Plot hole: Everyone is by Jack to try to help with the alien monster up his nose. By "everyone" we include the pilot and the copilot. Throughout the rest of the movie they wander about plenty times, both at the same time. The automatic pilot was knocked offline by the storm, and as Bob mentions in a later conversation, it was never fixed. So, who is driving the plane? Rhetorical question.
Revealing mistake: Jack is lying on the couch (whoever managed to fetch him back from the nest is anyone's guess) with an alien tentacle up his nose. The special effect used to display the invading organism swelling his brains is an obvious image morph that does not look in any way plausible visually alone - let's not even consider the glaring anatomical issues. (00:39:55)
Revealing mistake: Twice when both the couples of patrons are shown in their cabin and the camera pans from one to the other, right to left. Both times it's a fake panning shot with the wrong perspective in the CGI rooms, and in the second actual cabin you can even see the green screen. The first time around you can even see a door closed in one room and open in the adjacent one. (00:25:00 - 00:28:50)