Continuity mistake: When they are attempting to get "between the screws" of the tanker, the underwater footage shows twin screws, but the surface footage only shows wake from 1 single mid-ship propeller.
Continuity mistake: During the final chase scene, Captain Dodge says that it's overcast, and they surface. The first shot of the Stingray shows a hazy day. When the Orlando surfaces afterwards, it's clearly that one piece of stock footage of a Los Angeles-class submarine surfacing - not only is it sunny, but the ship shoots up from an emergency fast rise. After that, the shots of the Stingray in pursuit, and that of the torpedoes hitting the target ship, show it to be sunny rather than overcast. [It's not just stock footage of any old submarine surfacing. It is in fact the shot of the submarine in Tom Clancy's The Hunt For Red October surfacing - exactly the same footage. Some kind of in-joke, perhaps?]
Continuity mistake: At 1:20:35, when Dodge gives the order to "ready torpedo tubes one and two", both tubes are already showing "ready to fire" in the panel above Dodge's shoulder. (01:20:35)
Continuity mistake: Capt. Dodge (Kelsey Grammer) is on the deck of the sub and is sending a crewman up a ladder to attach a lamp onto the periscope. To attach it, he uses duct tape. However, when they show him climbing, the duct tape is still in Dodge's hand. Then, a second later, it is magically in the crewman's hand.
Continuity mistake: When Dodge is in his room talking to Lt. Lake, he throws the towel on his bunk which can be seen in the mirror. A few seconds later back on Dodge the towel is now gone from the bunk. (01:14:35)
Continuity mistake: When Grammer is welcoming his new crew on board, between the time the first crewman has walked up the gangplank and Grammer is talking to the second and receiving his papers and telling him to get on board, you can see that a third has already boarded and the number of envelopes held by Lt. Pascal (Exec. Officer) has jumped from one to three.
Continuity mistake: When Grammer is being taken by launch out to see his sub for the first time, you see between shots that he's going two different directions at different times of day. As they cut back and forth, one set of footage is a live shot, the other is against a screen. The end of the scene is a shot taken either in early morning or late afternoon whereas the preceding were more at midday.
Continuity mistake: When the Admiral asks Dodge how he likes his new boat, the pencil holder on the admiral's desk has three pencils lined up. After Dodge says, "It's a complete piece of..." the pencils have moved. (00:06:50)
Continuity mistake: During the opening sequences when the admirals are debating giving Dodge a command, Admiral Graham says that "three years ago" Dodge brushed up against a Soviet sub off Murmansk and that "as an ensign" Dodge got so drunk he ended up with his tattoo. Yet in two conversations with Lt. Lake Dodge says the tattoo came after the Murmansk incident.