Resolution Curiosity

So I already noticed with my map element in the other thread that the screen resolution affects how pixel positions are rounded off. When I was playing today, I also observed that at higher resolutions, pixels of objects don't move uniformly; every other row of pixels in an object takes turns moving. I normally wouldn't even notice, but my game focuses on tiny, uniform pixels, so it stands out. I figured since the game works perfectly at 800 by 600, there had to be something I wasn't taking into account when I raised the resolution.

So I suppose what I am asking, is does any ideas about why this happens or how to design for higher resolutions?