GetAwaiter(), that is used by await, is implemented as an extension method in the Async CTP. I'm not sure what exactly are you using (you mention both the Async CTP and VS 2012 RC in your question), but it's possible the Async targeting pack uses the same technique.
The problem then is that extension methods don't work with dynamic. What you can do is to explicitly specify that you're working with a Task, which means the extension method will work, and then switch back to dynamic:
private async void MyButtonClick(object sender, RoutedEventArgs e)
{
dynamic request = new SerializableDynamicObject();
request.Operation = "test";
Task<SerializableDynamicObject> task = Client(request);
dynamic result = await task;
// use result here
}
Or, since the Client() method is actually not dynamic, you could call it with SerializableDynamicObject, not dynamic, and so limit using dynamic as much as possible:
private async void MyButtonClick(object sender, RoutedEventArgs e)
{
var request = new SerializableDynamicObject();
dynamic dynamicRequest = request;
dynamicRequest.Operation = "test";
var task = Client(request);
dynamic result = await task;
// use result here
}