As a teacher, I think it is critical for careful correcting to be done as a matter of course. Students want credit for every correct answer. As a teacher,however, we all have made mistakes simply because we are human, and these are described as minor mistakes. I would tell students that if they found a mistake, to please discuss it with the teacher so that the paper could be corrected. I would apologize for the error made and then compliment them for looking at the paper so carefully. The idea is to make them aware that they are in charge of their learning in so many ways, and looking again at their own work is one of them.
The other issue raised is a bit scary to me. I have never seen any schools (10) in which I taught see this as a disciplinary issue unless the administration felt the teacher was truly incompetent.This question may involve union issues as well because of the threat of disciplinary action. Any teacher in this position should be advised to see the union representative for information.