I've been reading the wiki on melee weapons/attacks. From what I understand, with a skill of 50, you can do a special attack that generally does less damage, less DPS, and less damage per action point, for a little less AP. Does anyone ever use any special attacks? If so, when and why?

I use them. With a maxed out melee or unarmed skill you have access to several special attacks. I don't think I ever use the ones you're referring to (less dam, less DPS, less AP), but I often use the ones that take more AP but do more damage. The animations for these are fun and they work better on high DT enemies.