Bruce Wayne personally delivering a hearing-aid for a girl who he believes is deaf. Even if he was being lied to, the fact that he'd go out of his way to help her is adorable.
The flashback in "Traction," that shows Alfred picking Bruce up in the police station on the night of his parents' murder, is part this and part Tear Jerker.
Alfred: I can never replace them, Master Bruce, but I promise I will never leave your side.
In the episode "A Dark Knight to Remember" Bruce gets a hit to the head during a fight with Penguin. Unfortunately Bruce gets a bad case of memory loss, and forgets he's Batman. After getting attacked a dozen times, thoroughly confused by the way everyone has been treating him, and finally putting on the cowl without having a clue about being Batman. Seeing Barbara/Batgirl in trouble is enough to get him back in the field.
Batgirl comforting a scared Robin when they're on their own against Black Mask's minions in "The Breakout."
In the two-part finale of Season 4, one of the subplots concerns Bruce wondering if he isn't better off without Batgirl and Robin helping him. This leads to him continually leaving them out of the loop for most of both episodes. Finally, when the Joining finally attacks Gotham and Batman rushes off to stop them (leaving both of them behind, again), Alfred encourages them to disobey him, knowing he'll need all the help he can get. When they finally catch up to him in Wayne Industries, they confront him.
Batgirl: You picked us, Batman, because you knew we were strong.
Robin: And sometimes, that's about being strong enough to help you.
Batgirl: Even when you think you don't need us.
Batman: It's never been about not needing you. It's about not losing you.
Ellen Yin never much liked Bruce Wayne upon their first meeting, but the two came to see each other after Ethan Bennett becomes Clayface. But what made them be on good terms is in "Fire & Ice", where Ellen realized Bruce wasn't a "spoiled, arrogant playboy" he made himself out to benote Bruce thought she figured out he's Batman. She knows that Bruce really cares about his city.
In the same episode, Batman defeats Mr. Freeze and Firefly—saving the police from being frozen solid. Rojas still demands that he be arrested regardless. Realizing it was he who saved them, however, the assembled officers instead applaud Batman.
Joker and Harley's relationship, compared to other versions. Usually, Joker is abusive toward Harley (though there have been a few times that imply he does return her feelings) but in this version it's clearly more mutual. He even stole a diamond that was roughly the size of a softball for her for Valentine's Day. And even when it does look like they're veering towards the typical Joker/Harley relationship dynamic, it only lasts a few seconds, and he never lays a finger on her.
An example from the comics, crossed with Tear Jerker: After Batman and Robin arrest Poison Ivy in a facility, they demand to know what she wanted with the rare plant housed there. Ivy breaks down in tears as she says, "Do with it? I just wanted to see it!" But later, when she's back in Arkham, she gets a present — a picture of said plant with Batman and Robin's insignias on the gift card. She even cries and says Thank you for it.
At one point in the comics, Killer Croc falls madly in love with a reporter on TV. Needless to say, he goes on to steal various romantic items for her in an almost comical way. When he DOES get to her apartment room, he does his best to act cordial and nice. Even when Batman and Robin show up, he tries to keep his cool.
Killer Croc (while ready to bludgeon his foes with a chair): This won't take long, Meredith. I'll replace the chair.