I used to work in operating theatres. I've been told by a surgeon that taking out an appendix is easy, but from what I've seen I'd have trouble finding it in the first place! I'd definitely have a go at an abscess though.
Exploratory laparotomy is maybe an American term, in my hospital it was a diagnostic laparoscopy, where you make small incisions and use the camera to look around the abdomen. It would sometimes convert to a laparotomy, though.
Most of what's on Grey's, ER etc seems to be general surgery, but they never seem to cover the emergency urology or plastics cases!