Don\'t worry
You don\'t need worry a thing about your finger unless you just got cut recently, ask them to do it carefully, and if possible ask for a professional one to help you (normally in INS office, there is always a guy does better than others).
And you don\'t need to wait for the schedule day, when you got re-do notice, you can go there right away.
About my wife\'s finger print, I think maybe only one or two unable to clarify. But even this happened, you have to re-do.