Lots of good stuff in this thread.

What's your biggest weakness?

They want to know if you are self-reflective. If you say "I haven't thought about it much." Then they know you are not self-reflective. So be honest. I agree with tng. They see right through answers like "I work too hard." But if you say, "Sometimes I get so involved with one project that I ignore other deadlines and might let my team down." That's a more honest version of "I work too hard."

Here's something that has worked really well for me. Imagine as best you can what West Point is looking for. What kind of student do they want in 2015? Do they want their students to be ethical, to be respectful of all genders and gender preferences? Show an awareness of the sexual harassment issues at West Point in 2014. Do they want their recruits to be capable of leadership?

Then in the interview say this: I have an idea of what you are looking for. You want you students to be... and ... and ... Those are the qualities I want to bring to WP.

good luck.