During pillow talk Shinji confesses Asuka that he is afraid of failing her. She answers with this:
Asuka:"So I'll make you a deal, Third Child. If you, at some point in the future, let me down utterly, completely and catastrophically like you think you might, I forgive you in advance for it... providing that you don't mope around like an idiot for the rest of your life but find a way, any way, to make it right, and you don't stop trying until you do. Fair enough?"
During his first meeting with Asuka Misato is accidentally getting her angry, and Shinji thinks:
Shinji:"Asuka's mad at me. All's right with the world."
The story is chock-full of these, naturally. Shinji's atoner-complex and foreknowledge drives him to help out everyone he can this time around instead of running away and shutting everyone out. Shinji specifically protecting Touji's sister from being crippled by Sachiel's explosive death, for instance, leads to plenty of heartwarming moments that only Shinji himself can really appreciate, having experienced what would have happened otherwise.
Asuka and Shinji attending the school's dance.
Asuka sleeping together with Shinji to get rid of her nightmares, followed later by Asuka sleeping together with Shinji to get rid of Shinji's nightmares.
Shinji preparing to sleep in Misato's flat and realising how much he misses Asuka, sadly reflecting that he would have to wait four months for her arrival. Even the Asuka voice he suddenly hears in his mind telling him not to mope around and go to sleep because he has too much work to do sounds affectionate and concerned, hinting at their later relationship.
Shinji manages to get Rei to open up and actually live far more quickly and strongly this time around, to the point where they already feel like brother and sister to each other. Soon after convincing Rei that she is a unique individual that cannot be replaced should she die, Rei is put in a position where she faces extreme danger just to keep a promise she made and try to save her fellow pilot. She barely even hesitates before diving headfirst into a volcano with just a minute of power and AT-fields for protection.