The observable pattern (in the form of event listeners) is OK and is good practice. You see, even though RightPanel knows someone might be listening to all its events, it does not know who is listening. Well, technically, it could go through all its listeners and use reflection to find out who they are; now, that would be bad practice.
As it is, RightPanel knows someone might be listening to it, and that's all. Components are always aware someone might be listening, since the whole Swing is based on it. What matters is that RightPanel compiles without LeftPanel (or frame), and is completely decoupled from it, except via the listener interface. Not only cool, but standard.
As a side note, your class structure does not have to mirror your nesting panel hierarchy. Depending on what you are doing, it may be entirely fine to control behavior of both left and right panels from inner classes within Frame. (Personally, I'd use a JPanel, not a JFrame, since it allows for more flexibility, but this can be easily refactored). Otherwise, you risk splitting your View/Controller into too many closely coupled classes, and that would violate encapsulation and cause a lot of boilerplate code. Normally, I don't code big fat classes and try to refactor them into smaller ones; Swing is usually an exception. Better one big fat class than a maze of densely coupled classes. Unless of course you have a reusable component or some piece of functionality that can be clearly and intuitively decoupled; not just a couple of buttons or checkboxes that have no meaning in and of themselves. The simple fact that some subcomponents are situated within a certain panel in a component tree should not be a major factor IMHO.
For that matter, I usually don't nest JPanels; I use MigLayout and make all components into siblings. Matter of taste! I'd just encourage you to check out MiGLayout first and see whether you like it.