Yes, I am not able to play any music from the site at all. And yes, I know the browser could be an issue but I have gone through all the browser settings and haven't found anything which would affect to the problem. Recently, Nokia has also published Music client software (like Apple ITunes) and I tried also that but the same problem exists there as well.
As I am living in Finland I am using Nokia Music Store Finland instance
http://music.nokia.fi
But they have similar music stores published also in UK, Singapore, Australia and so on, you can find "select country" in the bottom of the music store main page.