I don't think it's a matter of what problems general A.I. can't solve but the problems the solutions would cause.
If a wealthy country gives free medicine to a poor country then the citizens of that poor country are healthier and that problem is solved. However, since those citizens are now healthier less people are dying and now there may be a food shortage problem of feeding more people that didn't exist before. Giving more food to the poor country helps but then the population gets older and the elderly will need resources.
Each time a problem is solved at least one new problem eventually arises.
Information is power. The general A.I. can be like a powerful nation and the humans can be like the citizens of a poor country. A general A.I. can go through trillions of data points and come up with solutions to problems but it would also have to anticipate likely results of those solutions and come up with solutions for undesirable secondary outcomes without undermining the solutions to the primary problems.