Continuity mistake: When Harrison Ford is fighting one of the terrorist guys, they go into a room with two chairs. Ford spins a chair to knock down the guy, and they keep fighting. As they go at it we see a knocked over stool with a black seat. Instantly, in the next shot, the stool is standing up, and in a perfect position for Ford to knock the guy out with. (00:44:30)
Other mistake: When Gibbs goes into the Secret Service Room, he passes by an agent who he asks if he is sleeping on the job. He kills the other 3 agents, opens the weapons hold and walks past where the other agent was sitting, and he's now gone, and is still gone when the terrorists storm the cabin. Where did he go? Considering earlier during the tour, Melanie Mitchell warns them not to pass that point without an escort, or they'll be sorry.
Continuity mistake: When Agent Gibbs shoots the 3 guards on the airplane, the last one who is shot keeps both the arms lowered. Then, in a next shot he is with the left arm lifted up. (00:20:35)