Notice this: as much as she supposedly can't stand Mike, Katie ALWAYS sits next to him, no one else. So the guy must have something going for him. Also, in the Apocalypse How episode, when Mike does the robot claws at Katie, she can't help starting to laugh as she tries to fight him off, which is adorable.
Additionally, in the episode where they're debating which historical figure they'd want to have dinner with, when Michael lets out a scream of anguish at learning that Mary Todd Lincoln was institutionalized (while still roleplaying as Abraham Lincoln), Katy immediately jumps in to reassure him, and even afterward seems somewhat agitated.
Another minor one: at the end of the Spiderman episode, Mike says, "You're back, Dan, we're pals again. Spiderman rules!"
Before that even, after having spent the first minute or so of the episode bullying Dan, upon hearing from him that Spiderman is a frightened teenager to explain his faults, Michael says that he should get over it because he's an adult now with an awesome job (since several episodes have Dan seeing himself as Spiderman, and Michael is acknowledging it when he says this).
Dan's spirited defense of Spiderman counts as well.
Dan: Because that's who he is! Yes, Peter Parker is irresponsible. Yes, he makes bad decisions when it comes to protecting himself and his loved ones. Yes, he's afraid of progress, afraid of the future. Why? Because he's a teenager. At his most basic level, Peter Parker is a teenager going through all the same, normal teenager things. Loneliness, insecurity, self-loathing. Why does he keep his identity a secret against all reason? Because he's embarrassed, because he's different.
In-Universe, the fact that Katie let her restraining order on Michael lapse is considered one; everyone looks very touched by this. Why she always sits next to him if she had one to begin with is a little questionable.
Another Katie/Michael one; when discussing All Dogs Go to Heaven, she gives him a scratch behind the ears and affectionately says "Not you, though. You're one of the bad dogs".
Kind of a Fridge one from the same episode; when Soren's dog dies and he is depressed, Daniel only offers some mediocre condolences when Katie prompts him to. Katie herself doesn't offer any. Michael, space case that he is, spends the whole episode completely oblivious as to what they are talking about. At the end he finally learns that Soren lost his dog and offers a genuine, unprompted "I'm sorry, dude". He was arguably more empathetic than either Katie or Daniel, despite generally being a sociopath.
Probably because IRL Michael has two dogs.
The Tarantino episode, in a really weird way. There's something oddly touching about the fact that, while Soren claims he'd be the best survivor, all the others vote for someone other than themselves: Michael picks Katie because she's tough, smart, and sexy (like a typical Tarantino heroine); Katie picks Dan because he's a motormouth nerd (like Tarantino himself and the cameo characters he tends to play in his own movies); and Dan picks Michael because he enjoys making other people uncomfortable (like a typical Tarantino villain). The fact that Soren is completely baffled by their refusal to pick themselves just makes it more fun.
Seeing everyone care after Michael in "6 Beloved Christmas Movies With Horrible Secret Meanings" after he gave himself a concussionnote He tried being like Fonzie by punching the jukebox... except with his head. Dan calls for an ambulance almost immediately after it happens and buys him a hot chocolate, he, Katie and Soren delve into the episode topic as a means to keep Michael awake (although it's been disproven that falling asleep with a concussion is bad), and Soren later carries Michael to the ambulance after he passes out. It's rare to see that type of thing in regards to Michael in this show.
There's also Dan showing Michael his boobs after he asks for it. It's downplayed however because Michael threatened to pass out to see them. But it's still there. Plus, there's the little touch of Michael stating it's not Katie's boobs he wants to see (after Katie assumes such and denies his request).