You need to use a delegate type that matches the target method. That can't be Action, that's a delegate for a method that takes no arguments. Fix:
Me.Dispatcher.Invoke(Windows.Threading.DispatcherPriority.Normal, _
New Action(Of String, String)(AddressOf RefreshDisplay), _
"foo", "bar")
Don't forget to actually pass those two arguments, I of course had to guess at them.