Continuity mistake: When Algren is sitting down with the photographer and talking to him, the old man with the pipe's arm changes position in between shots(the old man is standing next to Algren on the right).
Continuity mistake: When Algren and the samurai leave the village on horseback for the final battle, all the remaining villagers line the road and bow to them. You see Taka getting back up and when the shot changes, she's coming up again.
Continuity mistake: When Katsumoto's son gets shot and Algren rescues him from the bridge, watch the dribble of blood on his lip; it keeps changing lengths from down to his neck, to not there at all, to on his chin.
Continuity mistake: During the training scene near the beginning, Algren is showing a soldier how to aim and fire a rifle-musket. The soldier is looking down the barrel and is about to fire, but the musket's hammer is down (uncocked). The shot changes to the coloniel and we hear Algren talk to him. This lasts for a few seconds that are devoid of sound effects (ie. a hammer being pulled back). The shot then changes back with Algren in mid-sentence and we see the hammer is now cocked and a percussion cap has been fitted.
Continuity mistake: In the ninja attack scene, when Tom Cruise stabs a ninja in the chest, in one shot the sword is poking out his back, but in the very next shot, it isn't.
Continuity mistake: In the final scene Algren has his horse on his left. The horse changes to Algren's right when Algren confronts his girlfriend.
Continuity mistake: The scene with Billy Connolly holding a cigar when Tom Cruise is describing the scalping technique to Timothy Spall, Billy's arm goes from leaning on the chair that T. Spall is sitting in to holding the cigar mid-abdominal comfort zone several times. (01:00:00)
Continuity mistake: During the climactic horseback charge, Algren is shown holding his sword with the blade pointing upwards. There is, however, one shot, immediately before Colonel Bagley shouts "Aim", where, despite Algren's hand being visibly in the same orientation (so he's not twirling the sword), the blade is pointing downwards. Immediately after Bagley shouts "Aim", another shot of Algren shows the sword back in the upwards position. (02:09:45)
Continuity mistake: After Algren is defeated during the first battle with the samurai, Katsumoto says something to his second in command who kneels next to him, however in the next shot the same man can be seen kneeling down again.
Answer: The Battle of Thermopylae, see http://en.wikipedia.org/wiki/Battle_of_Thermopylae for more info.
Myridon