I worked as a nurse for many years, and boy did that teach me to be organized! I had to be or errors would be made. Now that I have my own cleaning business, I dont find I need a checklist, but then, I dont have (or want-) employees. What I do is thoroughly discuss the clients expectations with them before I clean their home. I try to find out how THEY see their home, what things bother them the most, so I can make sure I focus on those things.
If I had employees, I think a checklist is a great idea, and yes, it should be given to the customer. We can all improve on what we do, no one is exempt from that. Sometimes it is hard to get negative feedback (and sometimes its not justified-) but we have to be able to look at what we're doing and be willing to change.