Even though the Angel Fall arc is a marathon of Crowning Moment of Funny, there's Touma meeting his father for (from Touma's perspective) the first time, and Touma finding the picture of his family and finally learning what his mother looks like.
In episodes 19 and 20 when Accelerator takes a bullet to the head to save Last Order. Even if it doesn't redeem him.
Episode 24, despite learning that Hyouka isn't human, Index still loves her as she's still her best friend no matter what.
Out of all the people trying to capture, rescue, or kill Orsola Aquinas for her supposed knowledge of The Book Of Law, Touma was the only person who wanted to help her and didn't care about the knowledge. It certainly charmed her.
The final episode of season 2. Last Order wakes up in the hospital and asks "Where is he [Accelerator]?" After the frog-faced doctor's reply of he'll be back soon, she nods and says "Okay, Misaka wants to see him soon," before going back to sleep. An incredibly cute end to an action filled season.
Volume 15: Yomikawa talking Accelerator out of killing Kakine, saying that no matter how dark and cold his world is, she will drag him out of it, because to her he isn't a monster, just a child that needs her help. Even Accelerator himself was stunned when she succeeded. Of course right then Kakine stabbed Yomikawa with his wings, which made Accelerator fly into Unstoppable Rage coupled with Despair Event Horizon. And then Last Order appeared and stopped him with a Cool Down Hug, just like that, because she knew he would never hurt her.
Volumes 16: Kanzaki asking the Amakusa to help her fight Aqua of the Back.
Volume 21: Shiage Hamazura talks Acqua of the Back out of suicide and convinces him to keep fighting.
In the same novel, everything that the Pope does.
Volume 22: After 3 volumes of desperate searching for a way to save Last Order, Accelerator finally saves her using magic, and the first thing he does is embracing her tightly and saying "...Damn it, thank you... thank God...!!" Both of those are the last things one would expect Accelerator to do, but it just shows how important Last Order is for him, and it just makes you feel warm and fuzzy inside.
Shizuri Mugino calling Academy City out when she finds out that in the past they denied Shiage funds and basically forced him into the streets just because he was a Level 0 and assumed he was worthless. He may be a Level 0, but he was her greatest opponent, had earned her respect, and she's in love with him. Also, Shiage bringing Mugino back to sanity, forgiving her, and promising to help her reform ITEM.
NT 6: Mugino declares that her love for Shiage is not her weakness, but her strength.
Accelerator: Do you know what you need to do?
Accelerator: Then go. I'm not the protagonist here.
In the midst of all the chaos, Touma gets a call from his mother, saying she is all right and not to worry about her.
Touma finally asks Mikoto and Index to join him in battle. The two girls are really happy.
Doubling as a Tear Jerker, Kumokawa Maria finally come to terms with Kihara Kagun's death and decides to stay with him (more specifically, the Einherjar he has become) until he sees his selfishness through.
Kumokawa Maria: I have no choice, so I’ll stay with you. Just like leaving flowers by a grave, this is nothing more than self-satisfaction, but what’s wrong with one person being led around by this awkward will? I will not stop you anymore. Just like in Baggage City, you will probably wear away every last piece of your body to achieve your goal, but I will watch over you as you do so. Once you see this selfishness through until you cannot move a finger, you truly lose your human form, and you face true death as nothing but a pile of flesh, then we can return to our city.