I'm sure you're looking at the right place. Basically with pixel rounding, since it's always moving forward, if it gets in a spot where the x is actually between pixels it will move a pixel ahead or back even if the controls aren't touched since the speed isn't exactly 1 pixel per tick. Pixel rounding is doing exactly what it's supposed to do, and the fact that you're not noticing might mean it's pretty trivial, and no one else will notice either :P . As far as I know there's no way to prevent this besides redesigning how the level moves.

I was not using Pixel Rounding in the first link. Here's the link to the project. Thank You so much!

dl.dropbox.com/u/45336737/GentleShipProj/GentleShip0.1.capx

The blurring isn't fatal by any means, but if I can prevent it that'd be great.

I'm having a similar problem. I am using dt in my movements, so the sprite movement is very imprecise. If I use Pixel Rounding, the positions of the sprites bounce back and forth since they are moving with relation to dt (not a nice whole number usually). I can't think of a way to make the sprites not blurry and without rounding. Any tips? Even in designing sprites, perhaps?

dl.dropbox.com/u/45336737/GentleShip/index.html