Totoro finally realizing what the umbrella does. And then there's fact that it never occurs to him later on, be it when he steps into the Catbus and when he appears on a balmy summer night, to close the umbrella when he doesn't need it,
The Catbus' destination locator and subsequent meow "MEEEEI" is a definite "Aww" moment. FOREST HILLS > CEMETERY/SHRINE > MEI
Right after the Catbus helps Satsuki find Mei, it switches its sign to Shichikokoyama Hospital, offering to transport the girls to their mother.
The fact that the largest Totoro seemed absolutely delighted to be of assistance in searching for Mei, not minding a bit that he was awoken from his nap by a frightened human girl pleading for his help.