Every time I log in, I'm told that I have 1 turn waiting, but when I click on my games, there's nothing for me to play. Why is this?
It is a problem that many people have had for quite a while and Tom has not fixed it completely yet.
There is a temporary fix if you go to your profile page (Click on "Monty" to the left of the "1 turn waiting") in the bottom of the chart is "Current Turns" click on "Clear Cache" to the right of that.
This will fix it for you for now. If it comes back you have to clear it again.