Deliberate mistake: After Jim completes the awakening protocols, he is shown to his cabin because his door lights up. That's fine if he's the only one there, but he's not supposed to be. Presumably, there would have been hundreds of other people awakened as well, and the ship can't show all of them to their cabins by lighting their doors at the same time. But reviving every passenger separately and showing them to their rooms one at a time seems highly inefficient.
Deliberate mistake: When Sook-Hee is first shown her bed chamber, just after Sasaki leaves, she slides open the door to Hideko's room to look inside. After a 5-6 second silence, a thump sound is heard and Sook-Hee quickly closes the door. Later in the movie, when this same scene is shown a second time from Hideko's perspective, the thump sound, which is revealed to be Hideko banging her doll against the wall, occurs 11-12 seconds after Sook-Hee slides the door open. (00:06:38 - 01:32:33)
Deliberate mistake: The movie is set in the late 50s, but Howard Hughes is dealing with his plane crash and the senate hearing about the H-4 Hercules prototype. Those are events from over a decade earlier. However, it should be noted that the initial disclaimer of the movie is "Names and dates have been changed."