Design patterns are solutions for common problems. What problems are you having? In consulting work, we see that often when someone sets out saying "Okay, here's my idea. What design patterns can I put to work?," the architecture gets overly complicated very quickly.
Instead of looking for design patterns that you could possibly use, read up on design patterns (I hate to link to Wikipedia, but their article does have a good list to get you started on other searches with at least) and then apply them when you come up with a problem that fits their criteria.
As far as having a lot of code in your window class, that may be appropriate for your application, or you may want to look at something like a loose MVC pattern. Generally for GUI programming, a rigid MVC is going to be too strict, and require too much work for "true" separation of concerns.
There are many common problems that can be solved without design patterns, and that does not mean the solution is right or wrong. Plugin support, for instance, is very often given just by supplying a plugin interface or a set of events a plugin can respond to. Alternatively, you could look at the Adapter pattern.