After hearing from many that Power Users are still admin, I have converted myself to a regular user. Most apps continue to work properly. Remote Desktop stops working. To be specific, from the non-admin box, I can remote desktop to another machine, but not vice versa.
After fiddling with some settings, I discovered that regulars users are not enabled to remote desktop by default. After adding myself as a Remote User in the System Properties, I can start a Remote Desktop session to my box again.