The egg, and connections (spoilers)
dsb_mac made some great comments about this briliant movie.
But what was the significance of the egg? Near the end when Iguchi is going to have to go and fight, his children go off to school, then his mother goes out into the yard and picks up an egg, saying the chickens have laied in in the wrong place. There must be some significance to this?
A really good movie will have scenes where somethign happens, that has a connection to some later events in the movie. I think that according to the director, he movie was about 'change', i.e. this was the end of the samurai period. So as dsb_mac pointed out, when Iguchi met his friend eraly in the movie, the people praciticing using rifles (muskets) in the background were indicating that the world of the sword was over.
Later on, Iguchi said that he had sold his sword, and he thought the world of the sword was over. Then the irony is, in the end he dies by being shot.
Another connection, I think, is the scene where Iguchi asks Tomoe over to help him with his hair, probably with the main aim of asking her to marry him, but also to help him prepare for his battle. This reflects the earlie scene where he had been shamed, because he had being unkempt. He had promised never to do it again, so now he had to make sure he was properly attired with his hair prepared, before he could go to fight for his clan.