Problem 1: Use your new-found time to work on projects. These could be new companies that grow your wealth, endeavours that seek to create a change that you care about, or doing things to help people that you care about. There are other alternatives, too. Joining investment groups. Taking holidays. Consulting.
Problem 2: For chance meetings, I can see how this is a problem, but if you primarily meet new people through existing social circles, that might mitigate this effect a bit. I don't have this problem, but I have noticed that I've made lots of great friends through existing friends.
Problem 3: Could you not hire someone (or a company) to manage this sort of thing? I realize plenty of oversight would still be prudent, but it should alleviate the stress of it somewhat. Diversity in investments should mitigate the risk of losing everything. Limiting investments to areas that are well understood might also be a good idea for avoiding tax surprises.
I agree that wealthy people will definitely still have life problems, but I'm still not convinced it has to be these ones. Forms of social isolation (eg. imbalance that notch mentioned) seem much more plausible and nowhere near as easily remedied.