My greatest strengths have been covered in the other thread. As for my greatest weaknesses:
Organization. I am horribly, horribly disorganized. I often ad lib NPCs, combat encounters, and story hooks because I misplaced my notes. I don't know how many times I've arrived to DM only to discover that I left my campaign notebook - with today's adventure in it - back at the house.
Preparation. I often wait until the night before (or the morning of!) the next session to write the adventure. I might have had a hazy idea in my head for three weeks, but I won't write it down until hours before the next session. During the last couple of years I have been heavily into EverQuest, and there have been times when I simply chose not to write an adventure because I'd rather be playing EQ. Then I'd show up and wing it for 4 to 8 hours. I believe my players can tell the difference.
Rules Lawyering. I know just enough to get by. I don't study the DMG. I watch and learn when playing in other people's games, and I often pause a session to ask my players to explain a rule to me. If I don't know something off the top of my head and don't want to stop and ask a player, I wing it.
Obscure Story Hooks. I hate leading my players by the nose, so I will often throw a story hook out there and let the players flounder around trying to find it. This amuses me, but it can be terribly frustrating for the players, I admit. I also put in riddles and clues that are far out of reach given their current knowledge. More than one adventure have they failed to understand what's going on in time to do anything about it. I make it up to them by giving them big crunchy battles they can win.
Bad Judgement. I often make decisions or arbitrations that I later regret. I'm not good at making snap decisions and I often feel pressured to do so to move the adventure along. Sometimes I make stupid decisions that anger my players, and later when I review it I realize they were right to be angry.