Well it doesn't look bad at all 
Maybe simple straight lines would work just as well?
Unless you allow for semi-transparency, I don't think you can get anything better.
Corners: in the mockup view without rounded corners, it's just a matter of width: should be an odd n° of pixels. Just remove 1 px in height and in width, maybe a few stray pixels, and things should look good.
Same thing for rounded corners, plus some experimenting as to the best sizes for the circle arcs.
There are other issues in that mockup though. Next thread!
Oh Manupix...that's no mock up, that's a screenshot

So adjust the corners by 1px width and height? Gotcha! I'll give it a try!
EDIT: Ok now I'm paranoid, what other issues???
EDIT 2: Just so you know, I'm a programmer-spriter. So I will always need improvement

EDIT 3: I tried to use your advice and I failed to improve my corners. Could someone give me an example?