Theo discovering what Otis Amber and Crow do in their spare time...and because of it, choosing not to name Amber as his answer to the game.
Dr. Deere taking Chris under his wing, and eventually helping him get the treatment he needs to become healthy and a great ornithologist and scientist.
Also, Deere himself opting to forego the lucrative, yet medically-unnecessary field of plastic surgery in favor of neurology, where he can help genuinely-needy patients like Chris.
The note Westing/Sandy leaves in Ford's envelope: "Money owed for Josie-Jo's education: $0."
Related, although only in hindsight: Judge Ford telling Sandy that Samuel Westing not only paid for her education but made sure she got into the best schools, arranged for her first job, and possibly more. She completely dismissed Sandy's suggestion that the only thing Westing did was pay for an education her parents could never afford and she'd earned everything else herself.
Turtle going to meet Eastman/Westing.
"Hi, Sandy. I won!"
Turtle giving her Mickey Mouse alarm clock back to Madame Hoo. Also, her father starting to teach Madame Hoo more English so she'll cease being isolated is a subtler example.
Dr. Wexler breaking Grace out of her snobbishness and reminding her of happier days when she didn't worry about appearances all the time.
Really, Angela and Turtle's entire relationship dynamic. Angela is resentful of their mother micromanaging every aspect of her life while Turtle is resentful of their mother totally ignoring her in favour of Angela, but the two sisters clearly care about and love each other despite some inevitable feelings of jealousy. This eventually results in Angela pointing the bomb she set towards her own face in order to save Turtle from getting hurt, and Turtle willingly taking the blame for the bombings after she figures out Angela is the culprit.
Sydelle and Angela's partnership throughout the game. The two women are clearly lonely and don't seem to have any friends. They bond pretty quickly and get really into the game, to the point where they're doing all sorts of investigation techniques that most of the other players don't even consider. When Sydelle is injured by a bomb blast, the one person she wants with her is Angela. The novel even says she doesn't care what people think of her as she calls for her (which is a big deal, considering how much Sydelle worried about her image). And for her part, Angela goes with Sydelle despite her mother's insisting that she stay.
Crow's affection for Angela, even giving up clues to help her. It is so sweet, and kind of sad when you realize that a big reason was because of how much Angela reminded her of her daughter, who died and was forced into an arranged marriage like Angela.
Ms. Baumbach and Turtle's relationship. As partners, they are very nice to each other, and the two grow attached. When Turtle Takes The Heat for Angela, Ms. Baumbach takes her to the hairdresser, so she can get her singed hair cut.
Turtle and Sandy (Sam Westing)'s friendship. Sandy encourages her to keep playing, and Turtle never kicked his shins, which becomes a big clue later. He also took her to his dentist when she had a bad toothache, which actually gave her a clue to solving the Westing Game. Even after she wins the game, they continue to be great friends, and she is the one who sits next to him at his death bed when he dies for real. As you can see by all the spoilers, the relationship is a significant part of the plot.