In the censored version of the events leading to Jokers death, Tim immediately tosses the gun given to him by Joker to kill Batman aside, causing Bruce to smile with pride.
Moments later he jumps the Joker freeing Batman from Joker's grasp.
The following moment at the end:
Bruce: "Terry... I've been thinking of something you once told me. And you were wrong. It's not Batman that makes you worthwhile. It's the other way around. Never tell yourself anything different."
Don't forget the part right after that, when Bruce and Tim talk to each other for the first time in nearly 40 years:
Bruce: Hello, Tim.
Tim: Hello, old man.
It should be noted that the "old man" part was not sarcastic at all... which makes it even more heartwarming.
Subtly, bear in mind that the Joker really did die, and Harley was childless at the time. She moved on.
Not only that, but she really is pissed that her granddaughters were engaging in criminal activities. Not only did she move on, but she broke out of her own criminal mindset and wanted her family to be on the straight and narrow.
After being attacked by the resurrected Joker and his gang, Ace recovers by watching classic WB cartoons.
And Terry makes it a point to check up on him.
When Terry visits Tim in the hospital after the crisis is over.
Tim: For what it's worth, Bruce couldn't have chosen anyone better to put on the mask.