Factual error: When the jet fighter is flying by the naval ship, it gets shot down by a CIWS Phalanx system. The control panel used to fire it is not the real control panel.
Plot hole: There appear to be way more terrorists that take over the ship over the course of the entire film (if including all the different scenes) than what appears to have been able to fit on the helicopter (although Jordan mentioned it was full, the helicopter didn't look that big to hold everyone we see).
Factual error: The space amidships where the bad guys are supposed to be moving all those rails out doesn't really exist. Battleships were designed for compartmentation, with the largest interior spaces being the engine rooms. a space like that could fill with water and could easily cause stability problems. also, there was no provision for the 5 inch armor plate which comprises the deck above "broadway." A large open hole in this armor would have left the ship's machinery vulnerable to large caliber enemy fire.
Revealing mistake: When Seagal kills Tommy Lee Jones, he either sticks the knife into his head or smacks him on the top of his head with his fist (it's not that clear). But what appears to be clear is that this is in fact a dummy head or a stunt double - it looks very unlike Lee Jones.
Continuity mistake: During the final fight scene where Lee dies, Segal pushes his thumb into Lee's eye. If you pause the tape, you can clearly see Segal's thumb is bent inward.
Factual error: After taking the bridge and continuing down to kill the ranking officer, men are ordered to seal a door with a blow torch used for cutting metal, not welding.
Continuity mistake: Krill enters the Captain's room to get him to the party. Krill has a cigar in his mouth and when the camera pans to the captain instantly, Krill's voice says "I'm your date tonight captain" within a split second, with not enough time to take the cigar out of his mouth first.
Plot hole: When Ryback calls in to Admiral Bates and his people the first time he gives the size of the terrorist force at about 30. Now Ryback may be a badass SEAL but he is definitely not the best with numbers. 30 people including Krill would not be enough at all to run the operations of the ship including running the bridge, cutting the pieces necessary for the crane, running the engine room, not to mention all the people patrolling the ship that are looking for him after he has already taken out at least 5 of their men. So if they're getting this plan done, they're doing it with a hell of a lot more than 30 people.
Character mistake: When Rybeck gives Miss July basic instructions about the use of an Heckler & Koch MP 5, he calls it an assault rifle. This weapon is classified as a submachine gun (a machine gun firing a sub-caliber round). Someone with his training would know the difference.
Continuity mistake: At the party, you can see the cook standing next to the stage in one shot. Then, you can see him slicing a piece of meat on a table nowhere near the stage. Then, in the next shot, he's back next to the stage. Not enough time in-between shots to move the distance that he did.
Factual error: When Ryback uses a cutting torch to open the locked door and free the six sailors, he (correctly) puts on a pair of goggles first. Jordan Tate, however, just stares at the torch unprotected as he cuts through a thick metal door. While the exposure time that she experiences is fairly short, she never even flinches, and suffers no ill effects. Especially for someone with no experience with such tools, she should be wincing in pain and looking away or squeezing her eyes shut.