Continuity mistake: In the scene when Captain Phillips is telling members of the Navy that he is in Seat 15, a Naval officer writes the words "Seat 15" below "Captain Phillips" on the board. A scene or two later, the words "Seat 15" are to the right of "CAPT PHILLIPS." Also, "Captain Phillips" is now "CAPT PHILLIPS."
Continuity mistake: At the beginning of the movie, the scene where Captain Phillips and wife are in a car driving to the airport, Catherine Keener's hair changes back and forth between shots. The left side of her hair is swept back in a clip or comb. In some shots all the hair on her left is swept back, and in other shots there are loose curls hanging down. Flips several times.
Factual error: When Phillips is aboard the lifeboat, Najee has a pistol pointed at him at one point. The pistol is a 1911, and the hammer is forward when pointed at his head. Najee then fires it, but the hammer was forward the entire time until he fires the pistol. The 1911 is a single action handgun, and will only fire when the hammer is back.