Lord Asano telling Oishi that he will commit seppuku to preserve their clan and requested Oishi to look after his daughter.
Oishi's tender moment with his wife, in which he tells her that she must divorce him so that she can live, and he always loved her.
When Bassho was fatally wounded by the ambush set up by Mizuki, as he laid dying he confessed Kai that he was the one who threw stones at Kai when he was young, and he apologised to Kai for his actions. When he finally passed away, Kai closed his eyes peacefully while the other Ronin mourned the loss of a fellow warrior.
If you look closely at Oishi at that scene, he was slowly stroking the forehead of that Ronin, and he looked close to weeping when the latter passed away. It was through the actions of that Ronin that saved Oishi from the ambush.
The fact Basho's (the dying ronin) death is what finally has Yasuno (who was nothing but a complete jerk to Kai) to finally both apologize and thank Kai for saving his life against the beast early in the film. The fact he gives Kai Basho's sword as to mark him a samurai does much to redeem the man.
Mika sharing a moment of intimacy with Kai near the ending of the film. When Kai told her that he will look for her in the afterlife and whichever world he is in, she replied that she will be waiting to be reunited with him in every world he is in before they kissed.
The Shogun (aka Emperor of Japan) allowing Oishi's son to live to preserve his bloodline at the end of the film.
Technically the Shogun is not the emperor. At this point the position of emperor means very little politically or militarily. He does have all the power one would expect someone with the title "emperor" to have, though.
The Epilogue, in which the narrator states that the legend of the 47 Ronin lives on in tales told to future generations, and many actually came to Japan to pay their respects to the graves of the 47 Ronin on December 14 every year.