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.
Other mistake: In each film Segal plays a chief petty officer, who happens to be an ex-Navy SEAL. In the posters for Under Siege, he's shown in the dress white uniform of an admiral. In the second film he's still depicted as an officer, but he has been demoted to a lieutenant. I guess the producers just thought the officer's uniform looks prettier, even though they're the very same uniform, except a chief has anchors on his collar and no shoulder boards.
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.
Continuity mistake: When Steven Seagal is swimming alongside the submarine to place the explosive, the bad guys attempt to hook him. In one shot you see that they were successful with the piece of his wet suit caught in the hook and in a different shot you see his wet suit has been ripped above his right shoulder. As Seagal is climbing up to get out of the water, there is no damage to his wet suit.
Visible crew/equipment: As Ryback approaches the cake which Jordan Tate is hiding inside, a wire used to pull the cake away can be seen attached to the bottom of the cake. (00:41:25)
Continuity mistake: When Tommy Lee Jones is pointing the gun at the guy on the control panel, his glasses are intact. Just as the gun gets closer, the gun is actually touching his eye and the glass is missing.
Factual error: Early in the movie a F/A 18 is shot down by the Phalanx CIWS. At the time this movie was made, "Block A" models (shown in the film) could only engage targets that are head-on or close to it. It cannot track and engage a sideways moving target in the manner than it did.
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.
Other mistake: When Seal Team 5 was sent to the Missouri, according to the admiral, they were aboard a CH53E. The helicopter they were shot down in was a CH46.
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.
Factual error: The video feed form the cruise missile heading for Hawaii shows constant direction changes. If it was fired from way out at sea, it would just fly the direct route to its target, and it wouldn't have to change course a number of times.
Continuity mistake: When Tommy Lee Jones is launching the two missiles, he pushes the switches up one by one with his forefinger, singing "Five little Piggies". When he gets to the third switch, he places his forefinger on the switch, but in the next shot he pushes it up with his thumb.
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.
Suggested correction: Ryback is only going off what Jordan said about the helicopter being full. A CH-46 can only hold around 22 people including the crew. So his estimates were actually high. This is more of a plot hole for the movie since there is obviously more than that killed throughout the movie.
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.
Visible crew/equipment: When the bad guys enter the galley when searching for Cates and Ziggs, after they yell "clear" a boom mic is visible in the top left of screen. (00:46:10)
Other mistake: When the band is playing in the mess-hall you hear the drums playing along. When Ryback enters the mess-after after the take over, no drums are on stage.
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.
Visible crew/equipment: As Stranix follows Cmdr. Krill out of the hatchway, he looks around. As he does, the camera crew and boom mic man are reflected in his shades.
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.