As I observed last year in respect to this same strip, this is question of great interest to scholars of scalar predicates... also, there's an obsolete word "half-ass" meaning mule...

Intuitively, without reading any arguments, I'd say that half-assed is better than either no-assed or full-assed.
I'd interpret no-assed as not even trying or not even (or just barely) getting started. Half-assed is done and maybe even barely acceptable, even if it's underwhelming, while full-assed would be done completely and thoroughly, but wrong or badly enough that it has to be redone.

Let's apply this to painting a house.
A no-assed job would not have started a week after the first estimated completion time (or maybe they stripped the old paint but haven't applied the new coat).
The half-assed paint job is done but not a thing of beauty (and they didn't use enough drop cloths and they didn't do two coats on one side).
The full-assed paint job is done on time and reasonably well but in the wrong color (for example forest green when you wanted light blue).

of course, ymmv

The onager, or Asiatic half-ass, is not a mule; it's a different but closely related species, Equus hemionus. Onagers are slightly more horse-like than true donkeys, Equus asinus, so it's not surprising that someone could mistake them for mules.

This was touched on by The Simpsons in 1994:

Bart: No offense, Homer, but your half-assed underparenting was a lot more fun than your half-assed overparenting.

Homer: But I'm using my whole ass.

http://www.snpp.com/episodes/2F07.html

Michael, you succeded in making me to picture Homer with a crooked ass (and may be a doughnut in the opposite to "under-ass" half' hand, for balance).

Are you renovating? I feel your pain thru kilometers and ocean leagues. BTW, any paint job that isn't 2 layers minimum (first being a primer), is totally ass.

I know nothing of housepainting (obviously, it seemed like a good example at the time). Maybe because they've been painting the deska (lit: plank, a tall, narrow and long apartment building) next door for the last three months.
I'm not rennovating either, but just over a year ago moved into a new place (and dealing with handymen etc in this part of the world has cured me of wanting to move again for a loooong time).

When I was in law school, I once commented to a friend that although I was too tired to finish a writing assignment properly, I didn't "want to do a half-assed job." I then remarked that since I'd already half-completed the assignment with my full concentration, if I did a half-assed job on the rest, I'd be turning in a three-quarter-assed writing assignment, which wasn't all that bad. We coined the term "ass-fraction calculus" to describe this kind of computation.

My parents used the adjective "half-assed" when I was growing up and I never really thought they were saying something scatological -- I never saw it written down and came up with an intuitive understanding that it was spelled "halfast". When I saw "half-assed" written I thought it was somebody's scatological corruption of "halfast" and it took me a long time to figure out that it was not.

Aha, like my thinking, at 10, that the right spelling is Donkey's Hot. And believe me, I insisted, but the world didn't listen.

And while we're on this topic, will somebody please explain for an ignorant Brit the American expression "Ass backward". I mean, mine has been backward for half a century, and I find it works very well that way, so what's the problem?

I think the idea is that the ass is reversed (ie, backwards in a relational sense rather than the name of a particular direction); other phrases with the same sense are arse about face, arse on backwards, arsey-varsey, ass-end-to, ass-side-before, and back-end-to.

Freud could write a book on the displacement of 'half-faced' (imperfect, incomplete, OED) by 'half-assed'.

Maybe he did.

So, what colorful phrases do other languages have for half-assed work? I offer the Finnish "juosten kustu", which means "peed while running".

Polish has work done "na kolanach", literaly 'on (your) knees'. The idea is using your knees as a desk while you finish writing in the bus or streetcar on your way to hand it in.

That's how I did most of my homework in grade school!

ass this or that, in the end it be asinine

When I was a teenager, my mom and I tried to figure out "half-assed" and failed to guess why the "ass" was involved at all. I proposed that it might well stand for "half-fast" (fast in the sense of fastening), and Mom liked it so well that to the day she died, she maintained that was really the correct reading.

Jimmy's comment reminds me that in the town where I grew up, there was doctor named Dr. Halfast. He pronounced it "Hall-fast," but it didn't stop him from being the butt of jokes.

For "coined", read "pulled out of my ass".

Pararectal linguistification, perhaps?