community - How did Jeff become the Dean's favorite?

TylerShads' answer already covers pretty well where in the series we see evidence that Jeff is being favored by the Dean, so I will just add a bit of my view on the "why":

Throughout the series it becomes a running gag that the Dean is, lets say, a major oddball.

For example he dresses up regularly in strange outfits without any proper reason, more than often in woman's clothes too. In later episodes it also becomes apparent that he seems to have a dalmatian fetish.

It is also hinted at more than once that the Dean might be gay. We can see this for example in the interaction in his strange love/hate relationship with the rival Dean from City College.

In my opinion it is pretty clear that this is the reason why he has a soft spot for Jeff. He feels attracted to him and regularly makes remarks about how attractive Jeff is. An example of this can be found in the episode 3x12 "Contemporary Impressionists" where Jeff wears Aviator sunglasses and as soon as the Dean sees him, he falls to the ground screaming

Oh my god, even his shadow! Look at his shadow!

So in conclusion, I think the Dean likes Jeff so much because he is very handsome and the Dean feels attracted to him.