v1.2 has not been tested with ArcGIS Server 10. While many things will continue to work, there are new features in the server that the old client will not know how to handle. I would not recommend using v1.2 in this scenario but upgrade to v2.0. The nice thing about silverlight is that you just have to update the application on the webserver, and the users will automatically get the new application.
The upgrade path is as simple as installing the new 2.0 API, set the application to use Silverlight 4, upgrade the assembly references to point the new v2.0 api, recompile and publish the xap to the webserver. You will want to also upgrade the JavaScript so users who are still on Silverlight 3 automatically will get prompted to upgrade the plugin (in most cases this should already have happened through Windows Update).