From what I remember of my interviews, what the interviewers were expecting varied greatly. At Southwestern, the interviewers were looking for enthusiasm and attention to detail. At Texas Tech, it was pimp city for half of the interviewers, a sales pitch for the other half. Galveston seemed to have their minds pretty much made up and just wanted to see how you would fit in with the people already there. Baylor was looking for the more research oriented and seemed to taylor their questions to that end. Houston - personality and enthusiasm. San Antonio - Down to earth candidates to match the very relaxed personas of the program. Don't remember much of the out of state ones, mainly because I knew I wanted to stay in Texas.
Be yourself but after having helped with last year's interviews, I will say that nothing detracts more from an interview than too many pauses, "uh's", "you know"'s, etc. If you haven't mastered your nerves by now, you may want to take a few practice interviews to get yourself more relaxed with the whole process.
On the whole, anesthesia interviews are more a get to know you type of situation than an intense job interview. Relax, have fun, ask good questions, and don't be afraid to hang around after the official time is over to look around or ask questions of the residents. They will shoot you straight more often than not when they are in a more informal setting. That is key to avoiding a program where you might find yourself in a miserable situation.