That's... only partially what I asked. If you get hit by a swung sword; where it cuts or not; it's going to bruise; even if the sword itself doesn't, the impact of the armor would. Tack on chain mail being notorious for catching skin where ever it can, and the armor almost guarantees some type of injury. The biggest issue here is, you're saying a punch can damage, but a blade slash is nothing at all. It doesn't have to cut; but if the fist damages, then the sword would at least bruise, if not still risk bone breaking depending on where you're hit.
As for the specialized; that wasn't what I meant either. Chain mail's biggest weakness; beyond the weight that you've accounted for; is that anything that can fit through the rings can harm you. Now, unless you want to say that the rings are impossible to break; which alone would bump this up a rank; you're going to have problems with kunai, senbon, and thin bladed swords. Also, arrows or projectile in general. You need to make sure the description reflects this.