The Baudelaire's developing friendship with the triplets. Espicially what implicitly went on between Violet and Quigley in The Slippery Slope (even though, this being the series it is, she then never sees him again).
From The Grim Grotto: "When you think of me, think of a food that you love very much."
The Baudelaires meeting their Uncle Monty for the first time. After a horrific time living with Count Olaf, they find themselves with a kind guardian who gives them jobs based on their interests, arranges for them to join him on a snake-studying expedition to Peru, gives them run of the house, makes cake for them, and takes them out to the movies every evening after dinner. Unfortunately, we know it isn't going to last.
The implication that at least one and probably all the Baudelaires survived after everything they went through. A line mentions that Violet would return to the Briny Beach which she hasn't done by the last book so she definitely survived while Klaus is said to have lay awake for years wishing he had made a different choice and Sunny is mentioned to be reading her recipes on the radio
One does find Lemony's determination to write all the events that happened to the Baudelaires in dedication to his deceased ex-lover pretty heartwarming, in a strange sort of way. Also the fact he dedicated every book to her, even The Beatrice Books:
In The Beatrice Letters, Beatrice (Kit's daughter, not Beatrice Baudelaire) goes on a search to find Lemony Snicket, her uncle, yet can't either due to finding him too late or Snicket hiding from her. In the final chapter, she apologizes for embarrassing him earlier in the story and asks for him to meet her in a restaurant. She also states if he doesn't wish to meet her, he can rip the letter. From the way it's placed in the book, it wasn't ripped.