When Andrew first looks in the mirror to see his new human features, he gazes deeply in the mirror, as complex emotions play on his face for a long while. He finally quietly tells Rupert, "Thank you" in the most understated way.
Blink and you'll miss it, but when Andrew adopts the dog late in the movie, he names it Woofy, the same name Little Miss named her stuffed-toy dog way back near the beginning of the movie.
On Little Miss' death bed, she still has the little wooden horse Andrew made for her, which was his first sign of individuality.
The Together in Death ending, of course, is both this and a Tear Jerker. The implication that the nurse is Galatea and has also gained individuality makes it more heartwarming.
Some Fridge Heartwarming: Andrew hiring Galatea is probably his honoring Rupert, who by that time is at least 170 years old and has probably passed away. Galatea would have been "orphaned" by his death as well, so she's essentially Andrew's adopted daughter. This is probably why Galatea calls him "the great Andrew Martin" - and this is someone who stuck her with a pneumatic drill!
A minor one: When Andrew is cleaning a room, he sees a spider on a web. What does he do? Gently place the spider on a bush of flowers. Aww...
The elderly Andrew's speech to the World Council on his request to be officially recognized as a human being:
Andrew: I've always tried to make sense of things. There must be some reason I am as I am. As you can see, Madam Chairman, I am no longer immortal. President Bota: You have arranged to die? Andrew: In a sense, I have. I am growing old, and my body is deteriorating, and like all of you, will eventually cease to function. As a robot, I could have lived forever. But I tell you all today, that I would rather die a man, than live for all eternity as a machine. President Bota: Why do you want this? Andrew: To be acknowledged, for who and what I am. No more, no less. Not for acclaim, not for approval, but for the simple truth of that recognition. This has been the elemental drive of my existence, and it must be achieved if I am to live, or die, with dignity.