Getting Silverlight to work on Mac OS X Yosemite
Solution 1:
Under Safari/Preferences/Security click the last box that states "Internet Plug-ins: Allow Plug-ins"
So simple and it worked for me running Safari on 2008 MBP with OX X Yosemite
Solution 2:
I have been using some applications in the latest version of Yosemite with Silverlight and with Safari and never had any issues so I'd believe that this might be related to the application you're running on Silverlight.