I think, as the original poster put, the ability to keep your head down and say "yes mam" is a big one. At the risk of sounding sterotypical, I want to say that I've seen a lot of promising young men kicked out of some programs due to their inability to do just this. That being said, a lot of nursing schools have rules that feel like they came from the 1950s and they expect everyone to act like a proper young lady despite the fact that their classrooms are filled with fiercely independent women and even (gasp) men.
I also agree with the poster who said "don't take it personally" and I'd like to take it one step further by saying "don't let it eat you up inside." Someone forced you to take the wedding ring you haven't taken off in 10 years, you got kicked out of class for smelling like cigarette smoke, kicked out of a clinical for wearing the wrong socks, you have a quiz coming up where all the "right" answers go against every moral fibre of your being. The good students not only say "yes, mam." They find a way to get over the anger, the blow to your self esteen, etc and come back the next day with the same attitude they did in the first week of class.
Successful nurses also go to the right nursing school for them. Atheist at a Catholic College? At a school where minorities are treated "different"? Social anxiety in a school where study groups and group projects are mandatory? Have a mood disorder, or are emotional/more sensitive than most and going to a scool where nursing students are known to be seen crying in the halls and lounges on a regular basis? Find out about your prospective school and if something big doesn't match with you, find another one. If you're already at one with a similar problem, transfer out to one that makes it easier for you to be successful.
Keep yourself mentally healthy, follow the rules, keep your head down and say "yes mam," don't take things personally, go to the right school for you and you will be successful.
(All the examples in this post come from my own experiences and those that I've witnessed with my classmates. I did not make them up.)