The Doctor's excuse for not knowing what's 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? Doctor: Is that what that noise was? I was wondering.
Later he pulls a similar gag when Kensuke asks where the Doctor got the Sonic Screwdriver. When he replies "The Internet", Kensuke points out that the Internet hasn't existed since Second Impact, leading the Doctor to reply "That explains why it took so long. Never get the free shipping."
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 18 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 is 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.
Combined with Awesome, but Gendo's plan to deal with SEELE is to sic the Doctor on them.
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.
Shinji asks Asuka if it bothers her, breathing in LCL, now that they know where it comes from. After a moment, she replies that she was until he pointed that out to her.
After a very taxing day where the Doctor has had to explain who he is and what he's done several times, including people who tried to grill him again to try to figure out what he's really doing and where he's from (because extra-dimensional time-travelling alien who just wants to help everyone is not, shall we say, the most convincing cover story), he snaps and delivers one of his Badass Boasts when Kaji asks who the Doctor is. When Kaji just looks confused, the Doctor realizes that Kaji wasn't in shock of who he was - Kaji honestly didn't know because he'd been stuck in the elevator for several hours and genuinely didn't know who the Doctor was.
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).
Even later, Rei believes that Shinji hates her for her heritage. The Doctor explains that, in fact, his avoidance is actually due to the human incest taboo. Rei briefly ponders what this has to do with the situation, then upon figuring it out, discovers a new emotion: awkwardness. She doesn't like it.
Before ending up in Leliel, he's complaining that it's shown up during his regularly scheduled "Crazy Day", resulting in Misato having to repeatedly tell him to "Get in the damned robot!"
He gleefully calls out Asuka when he realises that she's projecting on him.
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 swimsuit with an arrow pointing to her breasts drawn on it. Leliel!Shinji admits that she wasn't exactly the best example to choose.
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?
Which is arguably also awesome and heartwarming, in that Shinji manages to force Leliel to end the vision, and that, while the various nightmare potential futures aren't enough to get Shinji to force a vision to end, the idea of being intimate with his sister is. For all of Rei's fears of being rejected, hated, and feared for her origins, Shinji truly views her as his sister, regardless of what species she is or how she was created.
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 meyou'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.
