In that light (no pun intended), the part from episode 23 where Higuchi is caught is also pretty heartwarming, as by this time, all but six of the police had quit because they were afraid of Kira, one quit because he was suspicious of L, one was killed, and one quit because he was not happy with L testing his resolve to stay. Light appears surprised at the police's cooperation, and then he and L jointly realize that the police were led in this action by the two who most recently quit, who subsequently return to the task force.
Perhaps this a strange moment to like, but there was something oddly heartwarming about one part of 'Ridicule', which takes place at Christmas. The task force are still slaving away to catch Kira, Misa's getting drunk and depressed, the 'three Kiras' are committing more acts of mass murder, and there's very little goodwill anywhere. But at the same time, Near is celebrating the holiday the way it's supposed to celebrated - playing with his toys (admittedly, he does that anyway) and hanging baubles on a Christmas tree.
"I feel you are the first friend I've ever had." L calls Light his friend, reaching out to another human being for what's probably the first time in his life. For a while it even seems like Light is reconsidering trying to kill L, then quickly becomes a Tearjerker when we see that he still wants to.
Although, considering that L was also lying when he told Light that...
Wordof God is that L was lying in the manga/anime, but in L:Change the World, it is revealed that in that universe, L did truly think of Light as a friend and is seen mourning him, since L outlives Light in this Alternate Continuity.
Also episode 26 of the anime is similarly both heartwarming and tearjerker-worthy Light misses Ryuuzaki. He's lonely without him around.
It's both heartwarming and sad because it shows that in any other world, in any other scenario, they could have been the best of friends. Alas, it was not meant to be.
It's worth mentioning that his missing Ryuuzaki is probably a little bit of Victory Is Boring coming into play too. Ryuuzaki was the only one who had truly challenged him on an intellectual level. Part of Light was probably missing the game.
In episode 25 of the anime, Misa in her Gothic Lolita outfit, walking and singing that song.
Misa's trust in Light in general is really very touching.
Unrelated to Light and L, but... in chapter 108, Near not only is calling all the survivors up again to keep working together, but if you look closely, there's that one shot of him playing as usual... and he's eating a bar of chocolate, just like Mello used to note Okay, you find a way to phrase that which doesn't make it clear that Mello dies.
Lil' Mikami. "Thank you, Teru!" D'awww.
In L: Change the WorLd, "You're a good girl. I believed in you", and "Maki, welcome home. Make tomorrow a good day too."
Late in the series, Soichiro tells his wife that he'll let her divorce him due to the trouble his involvement in the Kira case has brought the Yagami family. She is shocked and refuses, saying that she'll always stand by him, no matter how bad things get. He slumps in relief and thanks her. Seriously, who wouldn't want a love interest that was that devoted?
The task force going out to look for Light after he flees the Yellow Box Warehouse, especially since they defy Near to do it.
The conversation between Light and L on the roof and the subsequent slightly awkward foot-massage scene are oddly sad and heartwarming simply because out of context, it seems like L an d Light should be best friends - too bad Light's about to kill L.
The scene where Near asks Rester to escort him to Japan, because he's never boarded a plane alone before
The scene in the Yotsuba arc where Misa sits in Light's lap is really sweet.
The final conversation between L and Soichiro Yagami in the Last Name. L told Soichiro that the latter is a good father to him.
Aizawa's moment with his wife and daughter in the park after he quits the task force.
During the first movie, when they put cameras in Light's house L, in his usual position is half asleep. The first thing Souichiro does when seeing him is put a blanket on his shoulders. It shows that despite their views on fighting crime, he treats him no different than he would treat his own son.