Gallup states, "There are no weaknesses, just overdone strengths." Think about that statement for a second. In some areas you'll always be mediocre at best. Does that mean you just don't work on them? Here are a couple of suggestions:
Delegate. You are NOT superman/woman. Know your limits. In areas of deficiencies, ask for help (novel idea huh?) If you were great at everything, you wouldn't need to interact with anyone. You have a couple of areas you have the potential to be GREAT in. Develop those strengths and you will be successful. In other areas, you need help. What if you don't have the luxury of delegating tasks?
Study Success. If you HAVE to work in your weaknesses, find someone who thrives in that area and analyze them. Have access to them? Meet up. Don't have access to them? Research him/her. Everything includes a process, so learning "how" someone succeeds gives you a visual strategy. I'd caution you to copy, but it's an example to learn from. Success spurs inspiration. Turn it into action.
Complement Others. Find people that are the opposite of you. Different puzzle pieces fit together. For every weakness, there is a strength. That means focus on your strengths because someone else needs you to. It's easier to be around people that are similar, but leaders surround themselves with people who round out their blind spots. Put your ego aside and partner up.