Obviously Apple are fully aware of the success of the iPhone/iPod Touch (iDevice). They know how many iDevices they have sold and now with the introduction of the new iPhone 3G S and the lowered price of the iPhone 3G, surely they expect to sell even more, loads more. As the scope of the iTunes Store keep growing the need for an interface update becomes increasingly clear.
For me, the following improvements would be a good start:
Tab Enabled Browsing
Why not allow the user to open multiple tabs when shopping? When a search returns a list of items it is very inefficient to keep jumping back and forth between the item and the search result. Alternatively, allow the user to select either list, grid og Cover Flow to browse the result.
Introduce Recommendations
I am not sure if Sieglers suggestion to add an App Genius would be the best solution, but the App Store clearly needs some new and innovative way to assist the user and personalize the App Store experience. Integrating meta data dressed in a great user interface would be nice. At the very least the ability to search based on user reviews (star count) should be added. Adding an Amazon like “Users Of This App Also Downloaded” recommendations panel (that can be easily hidden/disabled) would also improve the Store experience (more transparent than the Genius recommendations).
Improve App Store Navigation
Sometimes I wonder if I am the only one that find the tiny buttons in the iTunes Store impractically small. When a search returns several pages of hits, the buttons to go to the next and previous page are tiny.

Tiny buttons: Why not make the buttons larger?
On the other hand, why not add keyboard navigation throughout the iTunes Store? Allowing the arrow keys to navigate between the different pages? Clicking would set focus to the frame that should be keyboard or scroll wheel controlled. Currently the iTunes Store behaves like a web page and not at all like a dedicated application.
Again I think list, grid or Cover Flow layout could add some value, or maybe something similar to CoolIris. Either way it would be a very efficient way of navigating the search results (of course with rating and description as part of the flow), and in my opinion clearly an improvement.
Customizable iTunes Store Front
To be able to customize the iTunes Store layout and content would be nice, just like in iGoogle: adding and removing content depending on what the user want and need. If a user is not interested in music at all, why should music suggestions occupy that much screen real-estate? Why not allow the user to select the order of the tabs of the “New Relases” so that eg. Apps are shown as default when the Store is loaded? The iTunes Store needs to be user customizable by drag and drop in much the similar way as the toolbar is customized.
Include the Icons in the Application Sync List
Given some guesstimates and calculations, each user have about 25 apps downloaded to their iDevice. With such a number, the list of apps in the library is easy to manage.

Missing Visuals: The app sync list needs to show the app icons.
However, it would still be nice to use those beautiful icons when selecting which apps to sync. This is especially true for the avid downloader with several hundred apps in their library, many with similarly sounding names (eg. Blue Attack, Blue Defense, Blue Skies). If I want to change my app selection I currently need to visit Applications in the iTunes sidebar simply to remind myself what the different apps actually are so I can add or remove those I no longer need. Adding the icons to the check list would provide the visual cue needed.
Currently Apple is not making it easy for their most active app consumers.