At the Navy administration building in San Francisco where the trial takes place, most of the automobiles shown are post-war. Amongst these are a 1949 or 1950 Ford, some early 1950's GM cars (perhaps Chevrolets or Pontiacs), and what looks like an early 1950's Plymouth.
Willie witnesses a Firefall on his trip to Yosemite. The Firefall was suspended at the onset of World War II, and except for one night in 1943 (before the scene is set), was not re-established until after the end of the war.
Maryk, Keefer, and Keith go to a carrier as Admiral William F. Halsey's flagship. Whilst the carrier Enterprise did serve as Halsey's flagship early in the war, his flagship, by this time, was the USS New Jersey, a battleship.
When Keefer, Keith and Maryk are riding up the aircraft elevator on the carrier, F9F Panther jets are clearly visible in the background sitting in the hanger bay. The F9F Panther did not enter fleet use until 1949.
When the Caine is first seen, it has the very large peacetime numbers on the side of the ship, but it should have the much smaller war-time numbers on the side of the ship, as it does later in the film.
During the trial, part of a calendar is visible on the back wall. It shows April beginning on a Wednesday, August on a Saturday, and December on a Tuesday. The trial is taking place presumably in 1944 or early 1945. These dates did not fall on these days of the week in either of these years; the last time this had happened was in 1942. The next time it happened was 1953 - the year the film was shot.
Just before the Caine runs over the target towline, Queeq is on the bridge chewing out Willie and Keefer due to "Horrible" having his shirt untucked. The film shifts to show the target being run over, then immediately goes back to Queeg and company on the bridge - "Horrible's" shirt is suddenly neatly tucked in. (Seconds before, Queeq had even ordered him not to tuck it in.)
When Ens. Harding is leaving the ship, he informs Maryk, Keefer, and Keith about
the strawberries. The group shot shows the ship and equipment in the background.
In the individual shot of Harding, there is a blank wall.
During the first officers' meeting scene with Captain Queeg, Seaman 1st Class Urban enters the wardroom. As the POV switches from behind Queeg to in front of him, we see his left arm on the table (from behind) then on the arm of the chair (from in front) repeatedly.
When Ens. Keith arrives on the Caine, Lt. Keefer asks for his orders which Keith hands over. Lt. Keefer then gives them to a seaman who disappears with them. On the way to DeVriess' quarters, Keefer and Keith walk down a passageway and no envelope is seen in Keith's or Keefer's hand, yet when they walk through the doorway, the orders are back in Keith's hand.
Captain Queeg, played by 53-year-old Humphrey Bogart, is clearly far too old to have been from the graduating class of 1936. Based on this chronology, the character of Queeg would have to be about thirty.
When the old Captain is leaving the ship, he says that he cannot accept the watch as a gift, but a departure gift from crewmen is allowed, as long as it is a modest amount and no quid pro quo is implied. A gifted watch would fit that criterion.
At the court martial held at Naval Station Treasure Island in San Francisco, the date of the mutiny is given as "July 22, 1944", which is not possible for several reasons. First, the only storm in the Pacific on that date was Tropical Storm Peggy, which took place in the South China Sea west of the Philippines with maximum winds of no greater than 40mph. Second, the typhoon in the film took place immediately after Maryk, Keefer and Keith had gone to Admiral Halsey's flagship to personally present their complaints to the Admiral. At that time, however, Halsey was in Washington, DC, meeting with Secretary of the Navy, James V. Forrestal and Chief of Naval Operations, Admiral Ernest J. King to plan future operations in the Pacific Theater. Halsey did not return to the Pacific until July 27th when he arrived in Hawaii from the United States and met with President Roosevelt, CINPAC Admiral Chester Nimitz, and Army General Douglas MacArthur that day. In the Wouk novel, the date of the mutiny is given as December 18, 1944, which would have been historically correct as that is the same day the three US Navy destroyers in Halsey's fleet (Task Force 38) were lost in Typhoon Cora (aka "Typhoon Halsey"). During the Maryk trial, it is also mentioned that three ships had foundered in the Typhoon on the same day as the mutiny on the USS Caine.
In Wouk's novel, Queeg identifies himself as being a 1936 graduate of the United States Naval Academy, which would make his age about 30 when he assumed command of the Caine in September, 1943 (November in the film), or roughly a quarter century younger than 54-year old Bogart was when he played him. ("The Caine Mutiny", p. 131: After a moment of silent sipping De Vriess said, "You're class of '34?" "Thirty-six," said Queeg. De Vriess knew this. He also knew Queeg's precedence number, his class standing, and several other facts about him. But it was a nice point of etiquette to simulate ignorance. It was a courtesy, too, to place Queeg by mistake in an earlier class; it implied that Queeg was obtaining a command for which he was rather young. "They're moving you fellows up now pretty fast.") In the screenplay, Queeg states in his wardroom meeting with the Caine's officers on the day he took command of the ship in Peal Harbor, that he had spent the previous seven years (1936-43) serving at sea in the Atlantic, which included the first two years of the war. ("I've had seven tough years in the Atlantic. Believe you me they made the last two mighty interesting. The way those subs ganged up on us I thought they had it in for me personally.") He later also tells Maryk and Keefer that he had been "a lowly Ensign on a cruiser" at the time of the stolen cheese incident in 1937.
When Queeg re-enacts ladling the strawberries from the bucket, he uses sand instead. Each scoop evenly fills the ladle to the top, i.e. there's no mounding. Strawberries wouldn't settle like sand, so a serving would have taken much more volume from the can. 24 servings took 3 quarts. If even a little bit had mounded up on each serving, the can would have been empty. Since no one, to this point, ever actually confirmed there were any strawberries left, it's strange that no one provided Queeg with such a reasonable explanation as to where the strawberries went.
The Jones, the ship the Caine is trying to beat back into port, is plainly shown trailing behind the Caine, as seen from the latter's port side. Yet, when Maryk tells Keith, "The Jones never saw the day she could beat us," the two men are looking forward off the port side, which indicates that the Jones had to be ahead of the Caine. Also, no ship is seen behind them, though the Jones and several others had been shown behind, just moments before.