The problem with being too open to regarded is that the teacher is inundated with frivolous requests. Grading is very time consuming, and regrading a test because a student simply isn't happy with the grade they earned is a horrible waste of time.

When I was teaching my policy was to reconsider anything a student felt was a mistake in grading, as long as it was accompanied by a written memo explaining precisely what the mistake was. I found this to be a good way to ensure I was getting legitimate regrade requests, since students would only put in the effort to write the memo if they really felt something was wrong.