I only had a quick look first time but now I played with it a bit more I found a significant problem.
If you have permanent cookies switched off, which I and many other people do, then when you add something to the basket it is updated on the page as being in the basket. However, when I click on the checkout button and it goes that page, it says basket is empty.
Methinks you need to put in some cookie checking to alert people that they must switch them on if they are off when they hit the buy button.
see:
Cookie Handling Routines in JavaScript