Corrected entry: The captain walks through the wheelhouse to the outer deck to water his potted palm tree. Even though the ship is at sea, there is no one on the bridge, and the ship's wheel can be seen through the window, moving back-and-forth, steering the ship by itself.
Correction: This is not a mistake: an unmanned wheel will turn if underwater currents apply sufficient force to the rudder.
Corrected entry: In the scene near the end in which Ensign Pulver reads a letter from a friend reporting the death of Mister Roberts, the friend writes that Roberts and another officer died during a kamikaze attack on their destroyer while drinking coffee in the wardroom. In real life, wouldn't the two have been at General Quarters during such an attack, not drinking coffee below decks?
Correction: This comment supposes that the ship was AT General Quarters. It's entirely possible that the ship Mr. Roberts was killed on was simply sailing and the kamikaze plane came out of the sun such that no lookout would have spotted them in time to sound General Quarters. Not all kamikaze attacks happened during regular battles.