I don't think it's strictly compliant, although they claim to have based it's syntax on Korn shell, which is the strictest definition of POSIX shells.

You can do pretty much everything in powershell that you can do in something like bash BUT, it will be done slightly differently, so trying to make a script cross compatible is pointless (you might as well just write it natively in powershell etc).

Powershell isn't inherently bad, unlike bash for instance which just allows piping out text output, Powershell can pass around true .net objects.
But if what you're looking for is cross OS compatability, you're pushing shit uphill.

99.9% of the time, I open powershell and just ssh into a "real" linux box.