When the hunter is fighting the bear, the hound jumps on top of the bear, and the hound rips a giant cut in the bears nose and shoulder. We then do not see the bear for a frame or so, but when we see him again, he is completely healed.
Disney tradition states that evidence of a wound can't be visible for very long. This is still a mistake, but that's why there isn't any wounds on the bear.
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