I never just show a movie. I would first ask why you are showing the movie. Does it relate to a lesson you are teaching? You need to make sure students understand that they are watching a movie for a reason. Tell them your objective for the movie, and what they need to do with it. As for what your objective is, that depends on why you show the movie.
There is much you can do with this film in a classroom setting. I think that more specificity will be needed as to what class you are teaching, what subject, the grade of students, and the end goals you wish to connect between your curriculum and the film. I think that the film is an excellent exploration into morality and human ethics. What constitutes moral action? Was what Mr. Hundert did moral in terms of advancing Sedgwick over a more qualified Martin? I think engaging in students in what defines moral action and how individuals should behave as opposed to how they do behave could make for a very unique and powerful teaching seminar with a rich and powerful film as its guide.
I am assuming you are going to show the movie and need ideas to include in a lesson plan.
Mr. Hundert is perfect for a character analysis and character trait lesson plan because he is the one character that experiences the most changes, reflects upon his situation, and is trying to make even further changes. This character is also good for a compare/contrast (before/after) lesson, and for an exercise on summary, based on what were his main regrets as a teacher.
Sedgewick Bell is a good character to do a reader's response where the student makes a connection (to self, text, or world) stating whether they have experienced a situation similar to him as a student with low grades, or if they know someone who has.
The rest of the students in his classroom sort of paid unjustly for Mr. Hundert's attention to Sedgewick. A good exercise would be to do a creative writing/persuasive piece where your students write a persuasive letter to Mr. Hundert stating why they should receive the same attention as Sedgewick. They can also write a letter to Sedgewick saying how they feel about his presence in the classroom.
Lots to do! Good luck!