Continuity mistake: When Captain Phillips is telling members of the Navy that he is in Seat 15, a Naval CPO 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." (01:28:05 - 01:49:45)
Continuity mistake: When Jordan goes to lunch with Mark, Mark is wiping his nose with a napkin as the waiter talks to him in the wide shot. As the waiter says the next word, they cut to a close-up of Mark, but the hand is missing the napkin and is in a completely different position reaching into his suit pocket. (00:08:25)