On Android 4, when touching the picker, a dropdown list appear on the bottom of the picker and when it doesn't have enough it appear on the top of it.
But when the picker is too down to see all the content of the list but not enough to make the dropdown list appear at the top, you have a list which is down the picker but not scrollable. So you can only select only the 2 or 3 first choices.
Test case with Alloy:
create a view containing this :
-scroll to the bottom of page and try to select other than the 2 first choices. If you just scroll a little up the dropdown list will appear at the top of the picker.
EDIT : Resolved! I managed to solve this issue when doing a simple test project, the problem was in the tiapp.xml.
In the android manifest part I have put the following tag
If you delete it or set it to true it is OK!
Strange link to the bug!