my biggest weakness is my inability to acknowledge how truly great I am. :-)
Maybe the best answer is that one's greatest weakness is being OCD about fixing one's weaknesses :-)
And for a serious answer: I spend too much time worrying about weaknesses when I should be delegating affected tasks to others while I focus on tasks that play to my strengths.
Or: If I don't do something well, I delegate it to someone who can and get back to doing what I do best.