How can I efficiently and effectively detect the version and, for that matter, any available information about the instance of Silverlight currently running on the browser?<
As mentioned in the above comments there is currently no efficient direct way to get the installed Silverlight version number (that works cross browser platform).
I wrote a post on how to workaround this problem and detect the Silverlight major version number (including version 3) programmatically and more efficiently using JavaScript.
You can find the code and the post at:
http://www.apijunkie.com/APIJunkie/blog/post/2009/04/How-to-programmatically-detect-Silverlight-version.aspx
Good luck!