Plot hole: Kingsley holds the only key card that can access the control room where the Captain is. He only has one card. He gives this key card to Rhodes so he can go up there and talk the Captain into not taking the sub to the surface yet, while Kingsley and his men head down to stop Scott and Taylor. When they employ the help of Marco and take out Kingsley and his men, Marco bends down and pulls the key card off Kingsley's neck so that now they have it... only Kingsley didn't have the key any more, as Rhodes had it and was still in the control room. A second key card magically materialized on Kingsley's neck.
Suggested correction: Kingsley only took the keycard from his neck to open the door and then hold it in his hand, so I guess he actually didn't give it to Rhodes. Just opened the doors.
Plot hole: When Wheeler and Cass are attacked by Kagan at the door to the bow several plot holes occur. Firstly, Wheeler lets Kagan live after defeating him in hand-to-hand combat as opposed to killing him, which gives Kagan the opportunity to recover and become a threat to the two once more, which he eventually does. It is also never explained how Kagan knew that Wheeler and Cass would be at that particular door to the bow in the first place and therefore be lying in wait for them.
Revealing mistake: When Taylor is playing dead on the floor, she stabs a man in the foot. Instantly there is already blood covering the knife and his shoe.
Visible crew/equipment: After Taylor is shot and Scott starts to help her up, in a shot down the hall you can briefly see one of the film crew ducking away off camera.
Revealing mistake: When Scott dislocates his thumb to get out of his hand cuffs, they are fully tight. But while he slips his hand out you can see the cuff is all the way loose to allow Van Damme to get his hand out.
Continuity mistake: When Ryan and Taylor are talking, she puts on a green shirt and her ponytail is still inside it. It cuts to a different angle angle and suddenly her hair is outside her shirt.
Revealing mistake: After Mel is killed, Scott drives away in a truck that they were just hiding behind during the shoot out. But there is not a single bullet hole or sign of damage to the truck.