Is it possible to run an application built on .NET 3.5 with a plug-in built with .NET 4?
You will need to rebuild (not exactly true, check update) the .NET 3.5 application to target .NET 4.0 because by default it will start in the .NET 2.0 runtime which will then not support the plugin.
If the machine only has .NET 4.0 framework installed the application will not run unless rebuilt to target it specifically.
Update:
Well, you don't need to rebuilt after all. Chris comment got me thinking and I just tested with a console application built for .NET 3.5. You can just specify in its application configuration file the following block:
If this is present in the configuration the application will use the .NET 4.0 runtime.