The Doctor's excuse for not knowing whats going on:
The Doctor: "Oh, I don't get out much, bit of a hermit and all that." Bystander: "You missed the gigantic aliens trying to kill us all?" The Doctor: "Is that what that noise was? I was wondering."
The Doctor's reaction upon learning that Misato keeps her sunglasses in a Disney's "Little Mermaid" brand case.
When Asuka accuses The Doctor and Shinji of being in "some sick pedophile thing";
The Doctor (towards Shinji, after denying the relationship): "You're not gonna take that personally are you? Bit of an age difference there, among other issues." Shinji: "That's not actually helping, you know..."
The prequel to Episode 7 opens with the Doctor trying desperately to remember some important problem that he needed to fix. After he finds Shinji attempting to bunk in the TARDIS for the night, he assumes that this was what he needed to handle and promptly tries to sort things out with Misato over a phone call. At the very end, he leaves the console room, only to come rushing back as it turns out the real problem was the TARDIS exploding and taking the planet with it. Which will happen in precisely eighteen seconds.
In Episode 8, after defeating the Angels, Shinji and Asuka are arguing in an elevator, when Rei walks in
Rei: (tilting her head) I'm... not quite certain how to interpret these sorts of things. Is it intended as an affectionate gesture? Asuka looks down. She and Shinji realise that his face his pressed up against her chest Despite being more than five hundred meters away from the descending elevator car, the acoustic sensors at the midway point clearly picked up the distinct sound of a slap
Soon after that...
Gendo:(cheerfully) NERV thanks you for your assistance with this matter, Doctor. If you enter this base again without my express permission, I do believe I shall have you shot The Doctor: And you really think that'd be enough to stop me? Gendo: I'd be disappointed if it did.
The Doctor preemptively stops Shinji from giving him the "Passive-Aggressive-Skeppy-McSkeptical" look.
The entire exchange outside the LCL plant after Asuka runs away, from Rei offering to literally drag the other girl back, to Shinji's exaggerated "Fiiiiiiiine", to Shinji running back immediately afterward to question why he suddenly understands German.
After stumbling upon the Rei clones, all of whom are naked, Shinji asks Misato and The Doctor if either of them plan to tell him to look away. When neither of them answer him, he eventually resorts to obscuring his own vision under a fez.
"You're both terrible role models, you know that?"
The Doctor eventually tells him that, as far as the DNA-equivalents that Angel flesh has are concerned, Rei is his sister. Shinji freaks out hilariously.
Specifically, he does this after Shinji asks him for advice on how to talk to her. It takes the Doctor a while to realise Shinji meant "How do I talk to a girl I have a crush on", rather than Shinji being afraid of what Rei is. All the while, the Doctor is trying to figure out what something he missed/forgot was, only to realise that it was the whole "Rei is Shinji's sister" after he realises Shinji has a crush on her. Shinji asks for some time in the Zero Roomnote A room in the TARDIS that is designed to assist with neurological healing, normal healing, and difficult regenerations.
Leliel!Shinji attempts to guilt Shinji for fantasising about a woman, asking him what the woman would think if she knew he fantasied about her. Shinji just points out that the woman they're talking about is Misato, who sent him a picture of her in a swim suit with an arrow pointing to her breasts drawn on it. Leliel!Shinji admits that she wasn't exactly the best example to chose.
When Leliel!Shinji tries to get him to admit that he cares about what Gendo thinks of him, Shinji agrees, but points out that it's a bit messed up that he didn't tell Shinji about Rei. Leliel!Shinji admits that it is pretty screwed up, and Shinji wonders if Gendo was "trying to set up a Luke-and-Leiasituation".
Leliel!Shinji keeps showing Shinji scenes of depressing or nightmarish futures, and fantasies about the various women he knows. Then it tries to show him one with Rei...
Shinji:NOPEno no no not going there stop it stop it stop. << scenario end >> Shinji:... what was that? Leliel!Shinji:What was what?
Near the end of Episode 12, after the Doctor and Shinji have saved Asuka, two NERV techs show up and try to take the ladder they had been using...
The Doctor:oi! Hands off! I promised Kongo I'd have that back to him! Tech: Sorry, sir, standing orders are to confiscate any material artifacts involved in an Angel incident The Doctor: Oh, come on! What're you going to do with it? Stick it down in the basement with some mystic mumbo-jumbo name? Call it the Ladder of Jacob or something?... Beat, techs glance at each other The Doctor: ... tell me you're joking Tech: They've... already printed out the labels
In Episode 13, Misato squees when she sees that Shinji has started to dress up like The Doctor