This isn't a bug within the game, although it is pretty important, and I wasn't sure where else to put it.
Just to check (I was bored), I decided to try and purchase an ad-free subscription (for one year), and I followed all the instructions until I got the screenshot below.
[attachment=12978:Screen Shot 2015-07-02 at 12.22.04 pm.png]
As one can see, there isn't any button, or indeed any link for one to click on to purchase a subscription at the moment. I'm not sure if this is a browser-specific issue; in that case I'm using Safari 8.0.6.