Almost Every heartwarming moment goes for the Jelly Trio's, showing The Power of Friendship very often. The most prominent ones:
In "Swimming Buddy", Raj has to deal with his acrophobia in order to be a shark with his friends. He almost surrenders, but when he sees a marshmallow with a "Congratulations" message, he gains enough courage to face it. And succeeds.
Also, in "Marshmallow Jones", it has the near ending on the episode, when Lazlo and Clam hug a "marshmallowed" Raj, and tell him they love their "marshmallow buddy". Raj, overwhelmed with happiness, tells them he loves them too and breaks down in tears. All together now: Awww.
Also, few moments show that Edward doesn't actually hate Lazlo and even likes him back. While Lazlo hugs him almost always, the moments when Edward smiles or returns the hug instead of angering is very heartwarming.
Lumpus' confession to Jane. Too bad he was in drag and her boyfriend mistook the confession. Hilarity Ensues.
The Rotten Bean Scouts telling Edward he's the greatest in "O Brother Who Art Thou", and Edward is moved by this remark.
The ending of 'Tomato Paste'. Edward is about to go to Tomato Camp after being accepted, and as a gift from all the campers, he's given a picture of him. Edward is moved to tears and that's what gets him kicked out of going to Tomato Camp.
Lazlo's devotion towards Scoutmaster Lumpus, even though he doesn't even like him back.