This is an issue that we faced recently in one of our sites where in only the admin user could see the sharepoint people picker control added on the page.For all the other users, the control was not visible and kept on giving the error:
"The control is not available because you do not have the correct permissions".
From the error , it seemed obvious that it was a permission issue.
We checked the group for the non admin user, also checked the people
picker which was set to choose from 'All Users'but it didn't help.
Eventually , the solution to this problem was found in the permission
levels.The permission level assigned to the non admin user was
'Contribute'. While checking the permission level settings , we found
that a permission 'Browse User information' had bot been given due to
which the users with the 'Contribute' permission level were not able to
see other users information and hence not able to see the people picker
control.
The solution was to grant this permission to the 'contribute' permission level.
Once this was done, the people picker was visible to all users.