This should be particularly obvious in the wet tracks that your tires leave after you drive through a puddle.
Not all problems with the tires are going to be in the tread. They can also appear in the sidewall. Fortunately, it's easy to do a visual check of sidewall problems. Look for tracks or cuts in the sidewall -- grooves that are distinct enough to be visible to the naked eye. This could be a sign that your tire is developing a leak (or worse, that it's nearly ready to blow out). This is definitely something you want to avoid. So if the cracks in the sidewall are starting to look serious, get that car the shop and start talking about getting them replaced. Better safe than sorry, as they say.
Sometimes the outer surface of the tire begins to weaken. The result can be a bulge or blister that extends outward from the rest of the surface. This is similar to an aneurysm in one of your blood vessels and you know that if your doctor tells you that you have an aneurysm, you'd better get to the hospital as quickly as you can before you blow out an artery. It's the same with your tire. This weak spot can cause a sudden blow out, and if you don't put the car in the hospital (or service center, as the case may be) before this happens, it may end up putting you in the hospital when the tire blows out on the freeway. So keep your eye on those tire bulges and blisters.