Towards the end of "Sydney, Australia", Simon, who used to be The Alcoholic, recounts what Sydney did after he came home from a giant bender in Australia. Rather than berating him for abandoning his family or falling asleep drunk on her couch, Sydney just left him a piece of chocolate cake and a card that says "Happy Birthday Dad. We Missed You." The simple gesture touched Simon so much, he's never had a drink since.
In "Dead and Improved", Simon is having a hard time eulogizing a jingle writer everybody hated. Instead he sincerely talks about the joys of having a daughter and receiving her unconditional love. Sydney knows that while her father is trying to comfort the jingle writer's daughter, he is clearly talking about her and is moved to tears.
On a meta level, Robin Williams and Sarah Michelle Gellar quickly developed an intense bond, with Robin providing Sarah with a paternal figure that she never had. The eulogy scene makes clear that the two shared a genuine affection.
Gordon's off-key rendition of "Wrecking Ball" to show Timothy he can be spontaneous and Simon jumping on stage to try and salvage the performance at Timothy's request.
In a meta one, Pam Dawber gushing about what a great experience it was to work with Robin Williams again after three decades. That she was able to do it before his death a few months later makes it even better.
A second meta-example. Robin Williams' death struck a lot of people hard, and tributes to him were flying thick and fast for days afterward. Sarah Michelle Gellar, who has repeatedly gone on record as calling Williams "the kindest man I've ever met," "a second father to me," and other similar lovingstatements, was still making them long after everyone else stopped.