Hi Mike,
2013-01-17 04:17:21 : *** Error: Unable to create file: C:/Program Files/PixInsight/bin/PixInsight.exe: Win32 error (32): The process cannot access the file because it is being used by another process.
This error message basically describes the cause of the problem: the PixInsight Core executable file (or another process attached to it) is still running when the updater program attempts to replace it with an updated version. Note that the updater program thinks that the PI executable is already not running; otherwise it would abort the update task just after:
2013-01-17 04:17:17 : Waiting for the PixInsight Core application to terminate...
It is very unlikely that this is a permissions problem, since the folder:
C:/Users/mwiles/AppData/Local/Temp/
is just your temporary files folder. This folder cannot be write-protected for obvious reasons. On the other hand, the PixInsight updater application is digitally signed with a code-signing certificate (as all the executables included in the PixInsight package) and runs in privileged mode using UAC (User Access Control) technology, so it basically is able to write anywhere on your computer without limitations.
The PixInsight application does not use the Windows registry at all (only the installation program writes a single keyword to the registry, to remember the installation folder), so this cannot be the problem either.
If you uninstalled 1.8 RC1 and re-installed 1.7, there should be no problems. Have you changed anything else on your computer since you installed 1.8?