Plot hole: The first time they communicate with the "entity" in the spaceship, they find a correspondence between numbers sent by the entity and letters of the alphabet. The entity presents itself as "Jerry". Later on, the entity tells Dustin Hoffman, "Stop calling me Jerry" - and then Dustin Hoffman realizes that the number-letter correspondence was wrong, and the actual name of the entity was "Harry". But if that is true, how could they have communicated without problems before? The very first word that the entity used was "hello", which would have to be displayed wrong, since it begins with an "h" and has an "e".
Visible crew/equipment: Beth attempts to convince Norman to inject himself with a tranquilizer by trapping him in a room and filling it with water. As the water rises, Norman frantically looks for a way out. There is a quick overhead shot of this scene that flashes on for just a second, and if you look around the perimeter of the room - you will see the entire crew, complete with camera and lights.
Continuity mistake: When Norman is running through the spaceship, he runs through a doorway and you get a glimpse of his facemask. It's dry. After going through water to get to the spaceship, wouldn't there be water on it? (00:43:10)
Revealing mistake: As Ted is being burnt by the fire, you can see his body trapped underneath the debris. In a side shot of Ted it is very obviously a stunt dummy as the left arm and head stay completely still and the arm remains completely stiff despite hearing screams and shouts from the pain.
Continuity mistake: When Norman and Harry are talking in the dorm after they hear of the storm coming, Harry is lying down in the bunk telling Norman how they are going to die. There is a shot of Harry's leg at the end of the bunk, then Harry sits up against the wall and in the next shot his leg is still at the end of the bunk, but wouldn't it have moved back when he sat up against the wall?
Other mistake: They're meant to be on rebreathers (they recycle the air around the system, so you 'rebreathe' it), yet in the u/w scenes, it can be seen that they're on open circuit systems, i.e. conventional scuba, as they're venting exhaust gases. Rebreathers do not release bubbles in the quantities shown.