I just had my bike fully fitted. Boy were my cleats way off. It actually felt a lot better in my knees and shins with them properly adjusted. He had to watch me on the trainer and adjusted the cleats at least 3 times before they were correct. Both of my feet are definitely not the same.
I would say that a professional fitting is worth it, not just for the cleats, but the whole bike. It's much different than the salesman/tech/whatever eyeballing it when you buy them.
Though, you might be able to find the right spot(s) on your own, as I'm sure many people do. For me though, what I thought was right, definitely wasn't.