1. Unpolished, imperfect, or unkempt, but generally able or ready for use or action. More commonly seen with "edges." This video is still a bit rough around the edge, but it's pretty close to what we want the finished product to look like. This old truck's a little rough around the edge, but it's still the most reliable vehicle I've owned.

2. Somewhat lacking in refinement, sophistication, manners, etc. The workers on the oil rig are a little bit rough around the edge, but they're damn decent chaps, every single one of them. Yeah, my local bar is rough around the edge all right, but I think that's what gives it its character and charm.

3. Somewhat sick or unwell, especially because one is suffering from a hangover. Bill: "So, I hear you had a wild night out. How you feeling this morning?" Ted: "A little rough around the edge, but not as bad as I thought I'd be."