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Just purchased Wing Commander Privateer from GOG, ran the installer, everything worked great up until the end.  

Installer seems to work well, I can see the files in the Virtual Drive, I tried to run DosBOX myself outside of Play On Linux, but I couldn't quite figure it out.

The error occurs when the installer is "Creating Shortcuts"  Internal Error: Expression Error Runtime Error then an access violation.  When I acknoledge it, I get a wine error and then the PlayonLinux Error in POL_Wine, Error in source, Error while installing archive, then the bug report screen.

Anyone have any ideas?  I'd hate to have wasted 8 bucks on Wing Commander. 

Yeah, running Windows DOSBox in PlayOnLinux does not always work.  I normally just copy the game folders to my "dosgames" direectory setup for Linux DOSBox.  Here is a DOSBox guide that might help you with setting everything up:

DOSBox Generic Guide

Here is a non GOG guide for DOSBox as well

Daggerfall DOSBox Guide