It's popular advice these days to "focus on your strengths," and not worry about your weaknesses. The theory goes that we should just focus on the things that we are good at and tailor our jobs to those strengths. If your not good at finance and looking at a balance sheet makes your eyes glaze over but you are great with customers and can't wait to get up in the morning and sell something to someone, focus on selling and leave the rest to someone else, right?
In general, this advice is sound and it may work for most jobs, but many leaders don't have the luxury to be that specialized. The higher you rise in an organization, the more broad your skill set needs to be and the more magnified your shortcomings become. A weakness that didn't matter earlier in your career may matter now, or it may matter at the next level of your career.
This is not to say that you have to work on every weakness you have--you only have to work on the ones that matter. I can't dunk a basketball or hit a curve; should I spend a lot of time working on those weaknesses? Of course, not; I don't play basketball or baseball so those weaknesses don't matter. If I were a minor league baseball player who wanted to go pro but I was weak on hitting curves; you better believe I should work to improve on that weakness. Effective career management, and effective management and leadership, is dependent on both capitalizing on your strengths and overcoming relevant weaknesses.
There is a simple reminder I always give to my clients--you get promoted for your relevant strengths and you get fired for your relevant weaknesses. You have to pay attention to both.