I am still having this problem as well, even after updating to iTunes 11.0.1, using a 2011 iMac and a Magic Mouse. Gestures work on every other app (Mac App Store, Safari, Chrome, etc.), just not the iTunes 11 Store.
EDIT: I have found a solution! http://discussions.apple.com/message/20443586#20443586 It appears as though changing your mouse/trackpad settings to "Swipe between pages: Swipe with one or two fingers" (two or three fingers on trackpad) solves the issue, and then you swipe with just one finger (two on trackpad) to navigate through the iTunes Store pages. I still prefer to keep my current settings (seeing as I don't want to accidentally swipe through pages with my one navigating finger), but that is a solution for those annoyed by the gesture issue.
Same for me : iTunes 11.0.1 / Lion - iMac 27' - 2011, the swipe between pages, on magic trackpad, works only with 2 fingers, but not 3. That was ennoying until I discovered this post! But there was no need to change any setting in the pref. pane, it just worked.
Thank's for the solution Exotic Car Man
Yes, I'm very cheesed off with this "enhancement" introduced by iTunes 11. Navigating through iTunes is a PAIN. None of the suggested solutions work for me as I'm still on Snow Leopard (the settings options simply do not exist and the Option+swipe actions I've read on other threads are ignored). Why does Apple like breaking things that work fine?