Caine is usually not too affected by enemies throwing mud, dirt, etc in his eyes. Of course not—he was trained by Master Po, who doesn't need his vision to fight, either. It also explains how he was so able to teach Serenity Johnson to rely on his other senses—this was training he received himself.
One episode has Caine get shot in the chest by an arrow, but he doesn't seem all that bothered. It's actually realistic: Most chest wounds aren't fatal because of direct damage to the heart (it's a fairly small target), but rather due to blood loss. He had spent the last several minutes, if not hours, in a meditative state slowing his metabolism. While painful, the wound wouldn't have been at all fatal as long as he got medical attention almost immediately.
