When Kapitän Jonas Herdt is stabbed in the back, there is no blood on his face. After he dies, there is.
When the cloth-wrapped bodies are handled through the u-boat, they are malleable. When handed up through the hatch, one is stiff.
Several times men are shown smoking inside a submarine, which wouldn't happen in WWII due to the fire hazard it presents. The air in a diesel/electric-powered sub (US or German) would be full of oil vapor and/or hydrogen from the batteries and extremely flammable. Smoking was allowed only on the upper deck for this reason.
All of the American and German submarines are shown to be using torpedoes equipped with proximity detonators which allow the torpedo to detonate when in close proximity to the target without actually hitting it. Although German, Britain and the U.S. experimented with magnetic proximity detonators at the beginning of the war they proved to be so problematic that they were quickly withdrawn from service and for the remainder of the war all parties relied on contact detonators.
While the sub is being submerged, several radio communications (voice and Morse) happen. While nowadays datagrams are possible, consuming a significant amount of time, during WWII subs had to surface, or at least go to periscope depth, to send or receive radio transmissions.
The German crew is often seen addressing the officers and NCOs as "Herr <name>". This is inappropriate, German military protocol requires all subordinates to address their superiors with "Herr <rank>".
Nathan Travers finishes his food revealing a swastika at the bottom of the bowl. This swastika, as a Nazi symbol, is turning the wrong way.
During one scene, a surface ship's crew is seen loading cannons. However, the shells being loaded are painted blue, which indicates that they're inert, non-explosive practice shells.
Mrs. Travers' LaSalle in the final scene did not have an A, B or C gasoline rationing sticker on the passenger's side of the windshield.
Because space and supplies were so limited on a U-Boat only the officers of the USS Swordfish would have been taken aboard the U-429 for interrogation. Very unlikely the crewman would be rescued too as they posed no value.
The US seaman shouts at the German "Stop the launch," to which the German responds in perfect English, "I'm on it."
The submarine shown on the movie poster is not a World War II submarine, but a Cold War era nuclear powered submarine.
WW 2 era submarines lacked the target acquisition and torpedo guidance technology to fight one another while both submarines were submerged. That didn't become possible until at least a decade after the war ended.
The German sub's 2WO (2nd Watch Officer) is wearing the uniform coat of an enlisted artilleryman of the German Federal Army. This specific design was not issued until the late 1960s/ early '70s and would not have been worn in WWII, and certainly not by a naval officer.
A Dymo label was shown on one of the USN ship's control switches. The Dymo label company (Dymo tape-writers) did not exist during WW2. It was founded in 1958.
Early in the film Chief of Boat Nathan Travers asks the men "Wanna talk some trash?". Of course, the term "talk trash" did not exist during WW II but is of more recent coinage (1981, according to Miriam-Webster).
The submarine shown in the movie poster is actually an Ohio-class nuclear submarine, not a World War 2 era vessel. The first Ohio-class submarine was commissioned in 1981.
Around 48 min. during the discussion between the German officers the microphone is clearly visible above the Kapitän's head.
About 30 minutes into the film, when Randall Sullivan (Scott Caan) turns away to vomit a microphone is visibly moving in the bottom of the frame.
On the USS Swordfish, the "medic" is summoned. In reality, a medic in the Navy is a "corpsman," which is an enlisted rating (job specialty). In the film, the "medic" is shown to be a lieutenant, someone who would likely be a doctor, but doctors didn't, and still don't, serve on submarines.
COB Travers refers to his bed on the submarine as a bunk. In the Navy they're called racks, and this applies to vessels and shore stations.
On the USS Achilles, the commanding officer calls for "battle stations." In reality, the CO would call for general quarters, which includes the crew manning their battle stations. The actual call announcing of general quarters is actually done by the Boatswains Mate of the Watch.
Admiral Kentz refers to COB Nate Travers as "Nate." That's improper protocol, as respect is expected to be shown both up and down the chain of command. The admiral should have addressed him as "chief" or possibly "COB." (COB is short for "chief of boat," who is the senior enlisted person in the crew.)