The most important thing a mentor can do is to have an overwhelming desire to see the person being mentored succeed. Make that, for the moment, as important as your career. Do not measure incoming people by the standards of your very best protégé. Accept the fact that some people are going to be less than perfect. Have a lot of patience, and be willing to spend a lot of time. The very best people need you least. Your minority students especially, and often times women, may need you badly at first, but tailor your programs to change as [your trainees] change.
The biggest tendency is to look down on people who don't have the skills you want. You must have high expectations for everyone. I don't think any one group is more gifted than another; work with everyone to bring people up to the level you expect them to ...
