Matthias Shapiro explains how to fix a problem with multiple ListPickers in a ScrollViewer.
Source: Designer Silverlight
The ListPicker is available via the Silverlight Toolkit for Windows Phone 7. If you don’t have it, you should get it. Get the source as well, for reasons that will be clear in one more sentence.
The only problem is that I can’t scroll if I do this because I run the risk of accidentally opening the ListPicker (which should be a tap interaction) when swiping (which is a gesture interaction).