I'm having the same issue as well. Looking at the iTunes "playing now" view in the window shows the infinite progress bar animation but nothing happens. A temporary fix seems to be hitting the Store menu's Sign Out option and then signing back in directly afterward. This will let it start playing again until it so chooses to stop.
Overall I like the iTunes radio experience but it has been buggy. There is a relationship with Safari in that if you do a reset to wipe out history and cookies, it affects iTunes which will then start asking you to sign in again. As a developer I do a reset on Safari to ensure I have a clean view of a site I'm developing so this can be frustrating. The last time I got it iTunes Radio working it was fine for a long time until I had to reset Safari and now it's having radio playback issues.