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.
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.
Factual error: The color guard at the end during the Captain's memorial has their flags in the wrong order. The American flag is always on the left as you face the color guard.
Audio problem: The two mercenaries Ryback kills in the kitchen have suppressors on their weapons yet you hear every shot as if the suppressors aren't attached.
Continuity mistake: During the show, after Bad Billy asks who's the highest ranking officer he lowers the mike. A shot later it's raised. A second later he repeats the question and the mike switches hands between shots.
Visible crew/equipment: Jordan arrives at the ship and Billy tells her "you can do this gig with your eyes closed." The whole crew is reflected on his sunglasses.
Continuity mistake: Right when Bad Billy introduces himself during the show his mike switches hands between shots.
Continuity mistake: When Segal is creating the distraction in the kitchen with the microwave, he pours liquid on the sponge. In the next shot the sponge is deeper into the cup. When he puts it in the microwave it jumps back out of the cup.
Continuity mistake: During the fight between Ryback and Strannix, Strannix cuts Ryback above his left eyebrow with his knife. The cut disappears shortly afterwards, but reappears in a later shot.
Continuity mistake: Early in the film, a missile is fired from the ship, and it hits the satellite installation right outside the Navy headquarters (the people in the control room hear the explosion). It gets there very fast. Later in the film, a nuclear missile is sent towards Honolulu. That is supposed to take 24 minutes. Why so long, when the other missile got there much faster?
Suggested correction: The satellite facility wasn't at Pearl Harbor, it was somewhere else. Based on the map it was located on a small island and the ship was very close to it at the time the missile was fired so took very little time to get there. The people in the command center, not control room, hear the feed go out, not the explosion. Many hours later, and after a lot of sailing, when the missiles are fired at Honolulu, the ship could have been a couple hundred miles away from Oahu so the flight time at about 550 mph would be 24 minutes.
Factual error: In the scene where Ryback is swimming next to the submarine, it is clear that the water is brown and murky. If the ship is in the middle of the Pacific, the water would be crystal clear.
Suggested correction: While Mobile Bay is the likely location, the Pacific Ocean is certainly not crystal clear all over.