We were able to track down the issue - the installer doesn't copy the files to the correct location if certain group policy settings are enabled. When this happens, you end up with a PTVS install that has repeated components in its path. The easiest way to
see whether you're hitting this problem is to check the existence of the following path (adjusting the disk letter and Program Files accordingly):
C:\Program Files (x86)\Microsoft Visual Studio 12.0\Common7\IDE\Extensions\Microsoft\Python Tools for Visual Studio\2.0\Extensions\
If this exists, then your PTVS install is broken in a similar way.
Until we fix this problem, the workaround is to run the PTVS installer under Administrator permissions, so that it does not have to elevate in the middle of installation. This can be done by opening an elevated command prompt (right-click -> Run as administrator),
navigating to the folder which has the downloaded PTVS installer, and running it by "msiexec /i <filename>.msi".