Ash father is a doctor, so when Ash says "goes doctor dad" I think he means that he speaks like a doctor (checking his breats). But that is only my guess, I don't think the comic is 100% clear on it, it's just what seems most reasonable to me.

About the comic
good things:
I like the writing of some of the story arcs.
The comic updates a lot.
There has been some development in the romantic / bad->good department, thinking about the main characters relationship that has been firmly established and Kate who even got a baby, though I think the second thing happened within the first 4 years of the comic and the other within the first 8 years.
not so good:
The plot goes extremely slow, you'd think ~5 pages a week would be fast, but many pages take place on the same day / evening, and so far the period of Ash' life hasn't changed (in high school, though I think it might be the final year), hence it doesn't seem like anything changes.
There are an extreme amount of comics that goes around in circles, the comic has been going for 12 years and has produced some ~3000 strips by now. I remember getting into it in 2008, reading through 1000 comics from 2004, that was exhausting, sticking with the comic for 4-6 years after that before I finally stopped re-reading the same plot in new shoes again and again.

What bothers me mostly isn't that the comic doesn't develop from the perspective of Ash & co. because as I see it there's not a whole lot they can do, what bothers me is that rumisiel isn't doing anything as far as I can tell.. at least the comic should change its environment once Ash graduates, but it's kind of bothersome that rumisiel doesn't try to solve his error. His brother also seem to have disappeared, I think last time I read it he met another angel, and more I don't remember.