The betas of new versions of the Nokia Store for both Symbian^3/Anna/Belle and for S60 3rd and 5th Editions continue to come. Today sees v3.3 of the former, with additional billing support and bug fixes, while the latter sees v1.3, getting better product description formatting plus the additional payment methods. Links below.

From the Nokia Beta Labs post:

Today we are offering members of the Nokia Beta Labs community a preview of the new Store clients for Symbian and S60. Please help us in testing them before they are deployed in a software update. 

The Store QML client for Symbian is available for Symbian^3, Anna, and Belle phones.  This release (3.30.005) includes:

• added additional billing support.
• error fixes, e.g. the client crashes when the user presses the search button during the start-up.

The Store client for S60 is available for S60 3.1, S60 3.2, and S60 5th Edition phones.  This release (1.30.004) includes:

• improved user experience by allowing longer product description
• added additional payment methods
• error fixes

Note that in each case you'll need to sign into Beta Labs with your usual Nokia account. On each of the download pages is a link to give feedback to the Beta Labs team, in case you hit problems.

Here are screens from the install of the S60 5th Edition version (confirmed also working on older devices such as the Nokia E71 and E72):