Dispatcher.BeginInvoke: Cannot convert lambda to System.Delegate
Since the method takes a System.Delegate, you need to give it a specific type of delegate, declared as such. This can be done via a cast or a creation of the specified delegate via new DelegateType as follows:
_dispatcher.BeginInvoke( new Action<MyClass>((sender) => { DoSomething(); }), new object[] { this } );
Also, as SLaks points out, Dispatcher.BeginInvoke takes a params array, so you can just write:
_dispatcher.BeginInvoke( new Action<MyClass>((sender) => { DoSomething(); }), this );
Or, if DoSomething is a method on this object itself:
_dispatcher.BeginInvoke(new Action(this.DoSomething));