A guy at Apple reports that there was indeed a problem with app store purchases, and it has been resolved. From my testing, this appears to be the case (I was able to successfully do a test purchase and download), but your mileage may still differ - so give it a go, and let me know what happens. You might start from a clean slate (quit and re-start the app).
Oh - I am also testing using the very latest version, which by chance just went live (although it may take a few hours to propagate). So even if it still doesn't work for you straight away, it'll be worth trying again after downloading the latest version.