The entire stay at the village. Though Katsumoto has a guard watch Nathan to make sure he doesn't do anything against them, they treat him more as a guest rather than a prisoner.
Algren puts on samurai robes for the first time and clowns around in front of Higen, showing how much he's relaxed around Taka and her family.
Later in another scene, while the family is having dinner, Algren asks for another bowl of rice in simple Japanese. Nobutada is... well, happy. And then the whole thing boils down to Algren learning the names of the family. Taka discovers later that Algren was learning from the children.
Within the space of a few short months, Algren grows to respect and admire the people he was hired to fight so much that he risks his life to protect Katsumoto and Taka and her family without hesitation.
Algren's relationship with Taka's sons, particularly Higen. Higen is old enough to understand that his father is dead and was possibly told that Algren was the one who killed him. However, during the ninja attack, he sees Algren struggling with an assassin and runs to get his father's sword, distracting another ninja long enough for Algren to gain the upper hand and finish them off. When you consider how important the sword was to the samurai, how no one else was to touch it and certainly not an enemy, that really drives it home.
When Algren leaves for Tokyo, Higen runs out to give Algren a scroll containing calligraphy that he presumably wrote himself as a present.
When Algren apologizes to Taka for killing Hirotaro, she accepts his apology, realizing he is not a bad person and was simply carrying out his duty, as was Hirotaro.
Katsumoto tells Algren that the Emperor arranged for Algren's safe return to Tokyo. Algren is then handed the Native American-style pouch that was taken from him when he was imprisoned.
Katsumoto: When I took this, you were my enemy
When Algren returns to Tokyo after several months as a prisoner, Simon Graham is the only person who seems truly happy at his return. Algren's other associates' reactions to his return range from detached surprise to suspicion.
Graham goes with Algren to the samurai village for photographs, showing how much Algren grows to trust the man.
Graham's last line about Algren's ultimate fate, that he finally achieved a measure of peace with his life, really end the film so well.
Simon Graham: As for the American Captain, no one knows what became of him. Some say that he died of his wounds. Others, that he returned to his own country. But I like to think he may have at last found some small measure of peace, that we all seek, and few of us ever find.
The ending reveals that Algren returned to the village to live with Taka, possibly they became a couple.
When Algren tries to bust Katsumoto out of prison, Katsumoto has fallen into despair and despondently asks how Algren plans to break him out. Enter Ujio killing the guards and a handful of other samurai attacking the compound. Even though Katsumoto gave up on himself, his people didn't.
Taka helps Algren put on her dead husband's armor before the final battle. Though she will never forget that he killed her husband, she recognizes that he's a good man and realizes that he has made a place for himself in her family.
When Katsumoto commits seppuku after he is defeated in battle, the enemy forces pay their respects by removing their hats and bowing to him in a traditional Japanese bow.
The emperor realizes the cost that has come from his dream of modernizing Japan and refuses a treaty deal with the US. He then seizes Omura's assets and gives them back to the Japanese people. The way he says "my people" is very heartwarming as well.