I currently have the 18-200mm kit lens for my canon 60D. I am thinking of getting the 10-22mm wide angle lens as a second lens. So far with my kit lens I havent experienced any focusing problems or needed any adjustments (so far as I can tell). Will the 10-22mm give me problems and need to be adjusted? Are there certain lenses to stay away from on the Canon 60D since it lacks the micro-adjustment feature?
Generally speaking I think the concept of "lenses that don't focus well on body X" is a misconception. All mechanical and electronic gear is manufactured to certain tolerances...and usually, the more expensive, the tighter the tolerances. If you get two pieces of equipment that are at opposing ends of their range of tolerance, you might end up having to adjust one or the other to get a proper "fit".
In the average case, most consumer-grade equipment is within a tolerance divergence that you won't need to do any adjustment at all most of the time, and it would only really be on the off-chance that you end up with a particularly poor match that you actually do need to adjust even to be moderately useful/acceptable. If you find that you regularly encounter lenses that need adjustment, its probably better to adjust the camera rather than the lenses, as its probably the camera that is near the limit of its tolerance range. Additionally, if you are really looking for a perfect fit with less chance of even a need to tune either the camera or a lens, you should probably be looking at more expensive equipment. Both lenses you listed are from Canon's consumer line of lenses, and are generally not manufactured to the stringent tolerance levels that the L-series lenses are. (The 10-22mm is a pretty solid lens, but its not an L-series lens, so I wouldn't expect it to have as stringent of manufacturing quality.)
Sadly, the 60D is the first of the Canon XXD line that I know of recently that doesn't seem to offer any micro-adjustment. My standard recommendation when people ask whether they should get a 60D or a 7D, given the moderate price difference, is to get the 7D. Not only does it have AF microadjustment, but it is packed full of a ton of other useful features as well.
I have the 10-22mm lens on a Canon 60D and it works just fine. As mentioned on the previous answer, because of the wide angle there is quite a margin for error in most circumstances — which won't show up on the finished photo.
The only lens I've had any focus problems with on the 60D is the Samyang 85mm f/1.4 (manual lens) fitted with the 'EURO' AF-Confirm chip. This fires the confirm-beep slightly short and while the chip is configurable, the steps between adjustable values are large and hitting the nail on the head at f/1.4 is difficult. In the real world, it's annoying but easily overcome by short-focussing the lens, pressing the button half-way, rolling the focus forward until it beeps and then rolling back just a hair. This does rule the lens out for high-speed action shooting, but I've found very little reason to take a f/1.4 portrait lens on a sports-shoot. Decreasing aperture helps, though (as it will on all lenses that don't get the AF quite right), and while it would be nice to have focal adjustment on the 60D, its other benefits still put it above the 7D in my mind.
If in doubt, tell your lens retailer what camera your lens is for when you buy it and ask them if it will work perfectly with that model. If they say yes, get a receipt and you have strong grounding to return the lens for a full refund if you have problems (as the reason you bought it was the seller's guarantee it would work, so if it doesn't then it's "not fit for purpose"). Good luck!
I haven't heard of any problems with the 10-22 (or with the 60D in general) but even if I did I wouldn't worry with the 10-22, as long as you're not shooting at the minimum focus distance your depth of field will be huge so accurate focusing is not a worry. In fact I once left my 10-22 set to manual focus all afternoon, I didn't notice because I was still getting focus confirmation beeps whatever I pointed it at (meaning things were in focus within the tolerance of the AF chip).
I got back focus problem with the EF 50mm f/1.4 prime lens on my 60D. It happens with auto focus, even with a tripod. The focus (I use the center point focus) always fall to the back of the subject. The actually subject is always blur.
And 60D doesn't have AF micro adjustment which makes me very disappointed in Canon.