Some AF systems have difficulty getting good focus with very wide angle lenses. Since the DoF is so large at wide angles it's easy to do a careful manual focus on the your typical critical distance of the moment (such as across the street) and leave it there. For general landscape purposes just memorise or mark the setting for infinity (or hyperfocal infiinity if you're really fussy).
There are two kinds of distortion on wide angle lenses. There is the natural inescapable "distortion" of a wide rectilinear perpective projection viewed at a narrowe angle (e.g. an A4 print 18" away from your eyes). This vanishes if you shut one eye anf bring the other close enough to the centre of the image to give the same angle of view. It's a feature of accurate rectlinear perspective projection and is the same for every lens of the sme focal length. It makes people at the edges of a wide angle group shot look fatter.
The other kind of distortion is the departure of a specific lens model from perfect rectlineariy, often barrel or mustache. This will make straight lines near the edges of the image look a bit curved. It's usually slight enough to be unnoticeable unless there are really straight lines near the edges of the image, not usually the case with landscapes, often the case with cityscapes or architecture. This distortion is very easily removed by an image editor which incorporates lens geometry corrections based on models of the distortions of specific lenses.
In the case of the Sigma 10-20mm it's mustache distortion. This has a linearly corrected centre and a slight droop from linearity at the edges. Some photographers prefer this because it makes people at the edges of a group less exaggeratedly fatter.
I used mine mostly for cityscapes and architecture. I found f8 a good compromise between good centre sharpness and pretty sharp edges. I found f11 gave sharper edges at the cost of slightly reduced centre sharpness -- a more even sharpness from centre to edge. I found the images needed a little more sharpening than longer focal length lenses. I'd probably still be happily using it if a nasty accident with a severe gust of wind on a tripod hadn't given me the perfect excuse to upgrade to the even better and wider Sigma 8-16mm