One thing to note about the 50mm F/1.8 is that it's a fairly cheaply constructed lens. If you touch the focus ring you should notice that there's some slack in it whereas if you use other lenses of a higher quality you'll notice that they are much more tightly constructed. While the slack in that part of the focus ring probably isn't directly relevant to the precision of the AF, it's a good indicator of the overall quality of the build of the lens and if you can imagine that same kind of precision on the AF motor then as you use AF you can see how it won't be as crisp as you might expect.

Two things you can do: use a smaller aperture (few lenses are their sharpest wide open) and refocus. If your focus has to travel very far then the momentum may carry it beyond where the camera intended for it to stop. So get focused once, then release the focus button (probably your shutter button) and refocus. The second time it shouldn't move very far, but probably will still adjust, and will hopefully come out sharper.

Also keep in mind that AF sensors are not perfect. The CEO of LensRentals.com has several blog posts talking about AF which are good reads if you're into details. The short version: even with the best cameras and best lenses (calibrated for each other) and under the best conditions, AF can still show an alarming amount of variation. Consider that you're using probably the cheapest lens on the market (though it has an amazing price:performance ratio, it's still quite cheap) and probably not the best camera available and you can see how you start noticing the imperfections.

Pat yourself on the back, your skill is outpacing your gear.

EDIT: Link to LensRentals.com blog - http://www.lensrentals.com/blog/2012/07/autofocus-reality-part-1-center-point-single-shot-accuracy