Factual error: Early in the movie when the interior of the downed aircraft is shown (underwater in Chesapeake Bay), with the eerie picture of Dutch's wife and the congresswoman's husband sitting underwater in first class with their hair waving slowly in the current, they are shown on the right side of the aircraft (the left side as we are looking at them, but the right side of the plane proper). Yet, when the airline representative is discussing this "problem" (non-married-to-each-other people apparently flying as a couple), they are announced as sitting in row X (don't remember), seats A and B. Aircraft seating is always done from left to right - i.e., the A and B seats would be on the other, or left, side of the aircraft.
Continuity mistake: In the scene in DC, when Kay is walking in the park and encounters Dutch on the bench, we see a man in a black shirt with red lettering walk by twice behind the shots over Dutch's shoulder. You can also see the man at a further distance in the background and then closer on the next shot.
Continuity mistake: When Dutch is leaving Kay Chandler's hotel room after speaking to her for the first time it cuts to a side view of him and you can see a door and hinges behind him, though in actual fact the hinges are on the other side of the door frame and there should be no door behind him as Kay Chandler is holding it open on the other side.