This may be way too basic to help people here, especially if you're like me and have been interviewed more times than you can count, but in my previous career one of my duties was hiring and interviewing applicants (pretty competitive almost 12-month process with multiple interviews, but not academic).
What I noticed was the most common (and easily avoided) mistake was interviewees not acting like real people. Being a little warm and convivial makes a huge difference, rather than coming across like a well-read automaton. Even if you're not going to be working directly with the person you're interviewing, there's still an aspect of "Would I want to work with this person?"
So for anyone who gets really uptight whilst being interviewed, that's my (potentially unneeded, fully unsolicited) advise.
Also if you're practicing with a colleague or friend first, I highly suggest also practicing being the interviewer. I honestly think the best way to learn how to be interviewed is to be the interviewer.
