IMHO not every startup needs to solve a problem. Most probably should, but entertainment is a viable reason for existence. Even so, some services simply lower barriers for socialization, which serves a need.
That said, I don't get Foursquare, etc. There isn't much entertainment there.
I too always question the "solve a problem" drum that everyone keeps banging around. These services are used to keep close friends in the loop and those friends can be between 1-100 years of age.
If you don't see a need or want to know where your friends are or, in Gowalla's case, what they are doing through pictures then you might need to rethink your friendship. Although it is cool to see what other people are up to that you might not know, these services are mainly tied to the close friends in your life, the people you care about and the people you want to spend the most amount of time with.
With that, I think that Facebook should concentrate on improving and designing a better core experience. Jumping on the mobile LBS isn't going to impress that many people. Plus the API is currently only read and although a rough time me table for write was given, Facebook has never been one to give out data all that freely.
That said, I don't get Foursquare, etc. There isn't much entertainment there.