Other mistake: Several actors/props/areas etc. are well known in this area to be flipped. For example, Billy Zane, who plays "Cal" in this film is right-handed, yet in some areas he uses his left-hand when it's not dominating and natural. (Noticeably, when he is chasing Jack Dawson down the grand stairs, he is holding his gun in his left hand, when it would make more sense to hold his gun in his right hand.)
Other mistake: After the "flying" scene, the story cuts back to real time. When it starts to transition back to the flashback, the camera zooms in on a television screen with the fireplace in it. This screen is 1) also used in the beginning of the movie 2) impossible, seeing how there was only one ROV in that room, and it shows the ROV in it.