Go back to the first episode, and just listen to the cheers and applause when Conan first steps out onto the set. Team Coco really missed him while he was legally prohibited from having a show.
At the end of Conan's week in New York, he officiated for the gay wedding of his costume designer on-air. It could have ended up looking tacky, or like a cheap ploy for ratings, but it came across as really sweet and heartfelt. You could see how much the two guys love each other, and how much Conan loves his staff.
Conan and Andy slowdancing. Sure, it was to parody the inauguration dance of the Obamas, but you can genuinely see from their expressions while dancing that they really care about each other. “It must be hard to do something so intimate, as to slow dance in front of the whole world”.
Yeah it's a set up, but the idea of Triumph using his insults to defend Jack Mc Brayer during their visit to Chicago's Wiener Circle is pretty cute, in its own messed-up way.