The same episode has Zack one credit short of graduation (due to dropping a class). The only way he can get it is to successfully perform in the ballet recital, but the recital is due to be canceled because of an illness among the original cast. The rest of the gang steps in to fill out the missing roles.
One episode has Kelly's dad lose his job at the plant right before prom, with her now being unable to afford to go. Zack then stages their own prom outside the gym, complete with cake, dancing, and a sign that says "Zack and Kelly's Prom" (the original prom theme, much to Belding's chagrin).
This ignores the obviousness that Zack's family is clearly wealthy enough for him to afford to buy her a ticket and dress (and in fact already did in a previous dance episode).
Not to mention that she's been seen several times in dresses that would certainly be suitable for prom.
The first episode of the high school years has a dance contest hosted by Casey Kasem. The first heartwarming moment occurs when Zack gives up on trying to get Kelly as his partner and instead chooses Jessie, who had been teaching him to dance.
The second involves Screech coming to Lisa's rescue. She injures her ankle and her original date dumps her, wanting to win the contest. Screech then becomes her contest partner, creates a new dance called "The Sprain" (where he and Lisa rhythmically limp around), and the pair wins the crows over, winning the contest over other finalists Zack/Jessie and Slater/Kelly.
The episode where Mr. Belding's brother Rod comes in as a substitute had one by Belding towards the kids and one by the kids towards Belding. When Rod ditches the kids' senior trip (which was changed from Mr. Belding's idea of sightseeing in a national park to Rod's idea of white water rafting) to hook up with a stewardess, Mr. Belding gives him an awesome "The Reason You Suck" Speech finishing with Mr. Belding telling Rod to get out of his school. He lies about it to protect the kids' feelings, then offers to take his place despite his lack of skills on a boat. The kids are overjoyed and thank him. Zack then reveals to Mr. Belding that he overheard everything, but tells him that while Rod may be the cooler Belding, they have the better Belding.
Mr. Belding might be the hardest on Zack but he's actually very fond of him and even names his son after Zack, who helped his wife deliver the baby when they were trapped in an elevator.
The episode "Fake I.D.s" has a few. Aside from the big one of the gang exposing Kelly to Jeff going out with another girl and Slater even offering to beat him up, a purer example happens when Zack, Slater and Screech initially get into the Attic nightclub and Slater explains to the college-aged woman he's set up with that he has a girlfriend, which she understands. What really stands out with this though is that as much as he and Jessie squabble at each other and he comes off as an insensitive jerk at times, how does he spend the evening? Showing the woman pictures of he and Jessie together and bragging about her. It's even mentioned that he has a picture of her from kindergarten. D'aww...
"The Last Weekend" ends on a particularly heartwarming note. First, after telling the staffers that he was proud of them and invited back to work for him next summer, Mr. Carosi pulls Zack aside and said that he had meant him specifically. Even better, he said he was a good man, that he approved of him and Stacy dating and gave him all the back tips that he stiffed him on for the breakfasts at the club.
Also a little later, as Zack is sitting on the beach sad about being away from Stacy, Jessie and the gang soon show up to walk with him and cheer him up, and if you look closely, you can see Screech and Kelly walk side by side and they soon put their arms around each other as well.
Any time the gang has a True Companions moment or episode, like in "The Lisa Card" when the gang helps to earn money for Lisa to pay back her father, they helping Zack get through knee surgery in "Operation: Zack" them coming through for Jessie in "Jessie's Song" (Narm quality of the episode, aside.)
"The Glee Club" competition has Screech rescuing Violet through a duet of "Beautiful Dreamer" with her, who was struck with stage fright and still upset over her parents barring them from being together due to his poor manners. Even if his performance was decidedly tone-deaf, his heart was obviously in the right place, and to top it off, her parents agreed with this and allowed them to date in the end.
Another episode of them in college has the boys helping to train Mike, their student advisor, for a tryout with a national football team, which also doubles as a Crowning Moment of Funny.
For a Fourth of July party, Zack tells Screech to come dressed as Uncle Sam. Screech shows up in Impossibly Tacky Clothes and says "This is how my Uncle Sam dresses!" The joke becomes heartwarming when you realize Screech's real name is Samuel. Screech's Uncle Sam might've been a bad dresser, but Screech's parents loved him enough to name their child after him.