Working with Edge Transport servers you may notice that cmdlets fail with an Access Denied error.
More specifically his happens with cmdlets that interact with the underlying application and operating system. Cmdlets as Get-ExchangeServer that just query the ADAM instance seem to be working fine.
The issue as well as the solution is User Account Control. Open an elevated EMC shell (right-click, Run as Administrator) and notice that all cmdlets work. For a permament fix the shortcut can be modified to alwas run elevated. Open the properties of the Exchange Management Shell and click Advanced, check Run as administrator.