Since I am my administrator …  I had to look into why AweSync was not installing on my freshly reimaged work Windows 7 PC.  I’d double click on the installer and it produced the error captured above:
”This advertised application will not be installed because it might be unsafe.  Contact your administrator to change the installation user interface option of the package to basic.”

I consider AweSync a trusted application, and certainly not unsafe.  So a digging we go.  Google wasn’t useful so I ran the install with the following command line:
   msiexec /i "awesync.4.14.0.msi" /lv c:\data\awesync.log
to get a installation log file.

Looking at the log file, the culprit was “ERRCA_UIANDADVERTISED”.  For reasons unknown, the default install settings for AweSync was preventing it from detecting Lotus Notes.  I don’t know why AweSync wasn’t actually installing but I expect that there was some old HKEY Current User registry information hanging around.  Remember how I said I had reimaged my PC?

Running the AweSync with the basic interface option seemed to fix the problem:
   msiexec /i "awesync.4.14.0.msi" /qb /lv c:\data\awesynca2.log

Update:
Since fixing the problem, the best explanation I’ve seen for why running the install with the basic interface option is this:

Running an installer with the basic user interface mode performs only the actions contained in the installer’s Execute sequence and bypasses the error noted above in most cases.
– Soumitra Mondal’s WebLog