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.
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).
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 villian). The fact that Soren is completely baffled by their refusal to pick themselves just makes it more fun.