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. Then, she saves Accelerator's life, even though she doesn't really care about him, and snaps him out of being a Death Seeker.
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.
After being put in a world where someone else is in his place, Touma declares that almost everyone he knows hated him at first, but became his friends and allies. He has no doubt he could repair his bonds with everybody.
It may have been cruel for Othinus to put Touma in a world that doesn't need him, but it was rather nice to see everybody so kind and happy, even the Kiharas.
The Will of the Misaka Network stops Touma from committing suicide, then tells him this world isn't perfect, because he isn't in it. After convincing him it's okay to be selfish and fight for himself, it tells him it will be waiting for him in the original world.
Even as he lays dying, Touma tells Othinus to use his Imagine Breaker better than he did. She is so touched that she instead brings him and his world back, choosing the original world he wanted over the original world she wanted.
Touma chooses to become the world's enemy if it means protecting one girl (Othinus). He even stops to think that he doesn't blame Index, Mikoto, and the others for not being able to understand his choice.
Touma remarks that if Othinus ends up arrested for her crimes:
He would have visited her countless times. No matter how much time it took and even if they had to wait until they were old and wrinkled, he would have made sure she was met with a smile when she finally was released from that cell. And once all of her crimes had been made up for, they could walk together in the light of the sun.
Mikoto picks up where the Will of the MISAKA Network left off and breaks the last of Touma's delusions about the Perfect World, helping him realize the value of his own world. Bonus points in that it comes with a literal heartwarming hug—she shocks him while her arms are wrapped around him in a victorious embrace.
Despite truly wanting to kill Othinus for endangering the world and threatening his loved ones in the process, Accelerator throws his fight with Touma, reasoning that if he, the #1 Level 5, were defeated so soon, Academy City would hesitate to order others after them.
Agnese decides to give Touma the benefit of the doubt and help him and Othinus escape the Agnese Forces.
After Touma defeats Marian Slingeneyer, he hands her over to Mjölnir, then gives Mjölnir his number, telling her to call him if she is ever in trouble, not even questioning her unusual appearance.
President Roberto Katze giving a heartfelt speech to the entire world and urging them to not give in to their fear and hatred of the unknown and urging them to give Touma his chance to redeem Othinus.