Heck, just seeing SpongeBob, one of the most famous cartoon characters of all time, on the big screen must have been so awesome for several fans.
When Mr. Krabs is trying to explain why he didn't give SpongeBob the manager position in the beginning of the movie, he's stuck on what word would describe him before he comes to "kid". The audience tries to help him find the word, but it quickly devolves to the crowd tossing insults at SpongeBob, at which point Mr. Krabs angrily tells them to stop. In general, Mr. Krabs clearly feels awful for SpongeBob when he sees how much he wanted the position and attempts to let him down as gently as he can despite having to be harsh, and it's a sweet instance of Mr. Krabs actually showing he cares about SpongeBob in spite of his negative qualities.
Near the beginning of the film, Patrick treats a depressed SpongeBob to several Triple Gooberberry Sunrises to cheer him up. Made especially heartwarming before SpongeBob notices the sundaes, as when he decides to go home and calls off the celebration, Patrick asks him if he's sure, and once SpongeBob says he's made up his mind, Patrick gracefully accepts SpongeBob's decision; then welcomes him back with open arms once he changes his mind.
Despite being angry with Mr. Krabs about not giving him the promotion, SpongeBob instantly snaps out of his cynical hungover state when he sees King Neptune attack him and attempts to defend him, stating that being manager isn't worth killing Mr. Krabs over.
Patrick's adorkable reaction when he finds out that Mindy knows his name. Fridge Heartwarming when you remember the early running gag about people constantly forgetting Patrick's name. Hearing that Mindy remembers must have meant a lot to him.
The whole audience in the movie theater — not just the pirates — cheering when the tear of the Goofy Goobers revives SpongeBob and Patrick.
David Hasselhoff doesn't even bat an eye at a random pair of marine life, in this case, SpongeBob and Patrick, needing help. After decades as a lifeguard, it's easy to imagine that Dave (or Mitch) has grown used to assisting his ocean friends when they need help.
SpongeBob's speech just before he uses The Power of Rock to undo Plankton's brainwashing on the populace of Bikini Bottom. Here he talks about how during his journey, he's learned that there is no escaping who you are, and states with pride that he managed to get King Neptune's crown back despite nobody believing he could do it, and SpongeBob finally accepts who he really is inside - a kid at heart. The music during this scene makes it even better, borrowing from the beginning of Whitesnake's "Here I Go Again". Doubles as a Crowning Moment Of Awesome.
King Neptune getting an aesop about showing love and compassion, and praising Mindy for being right, and apologizing to Mr. Krabs for falsely freezing him.
SpongeBob and Mr. Krabs' reunion at the end of the movie, and Mr. Krabs apologizing to the guy for doubting him.
He also says that he'll never doubt him again. Remember who is saying this, and to whom, especially after what he said earlier in the movie and throughout the entire series.
Even before that, Squidward did try to stop Plankton's Evil Plan despite his dislike of Mr Krabs when he saw that Plankton was selling Krabby Patties, whereas he could have easily done nothing. Sure he gets stopped by the Mind Control helmets, but he at least attempted to do something.
The end credits of the film definitely qualify. They consist of a montage of SpongeBob, now manager of the Krusty Krab II, working hard at the new restaurant and loving every second of it; set to the wonderfully-cheesy Ocean Man, by Ween. Sure, it's a simple ending, but satisfying nevertheless, and suiting of his character.
. Doubles as a Crowning Moment Of Awesome.