You can probably solo some of the level 70 shit. I haven't played a DK since Wrath so I'm not keen on how much self healing you boogers get. I know as a warrior I was able to solo Kara up to chess/netherspite but mechanics won't really allow for a single player to beat those. Also did a few bosses in SSC for transmog shit but didn't do all of them. Some of the bosses in BT/Hyjal should be soloable as well. As far as level 80, I've seen DK's solo some raids so it's possible. Heroics naturally though there's not much gold to be had there.
"There are no men like me...only me."