CFI interviews
I went through six CFI interviews. These go back several years, so I'll try to relate what happened as best as I can.
At ERAU, I took a written that was based on everything up to CFI. I believe I had a one-on-one interview with the Chief Flight Instructor. I had a group interview with the Chief Instructor and the three training managers and, finally, a flight in a 172 with the Chief Flight Instructor. I recall one question in particular during the group interview; what were my plans. My response was that my short-term plans were to get this job, for which I was interviewing. I had taken my MEI ride only the previous Thursday, which was extremely fortuitous timing, because I told them that and said to them that doing so should have proven to them that I really wanted the job. I was hired. It was a one-day process.
I had an interview with Comair. No writtens, perhaps fifteen minutes with the Chief Flight Instructor, and a flight with an Assistant Chief. It took barely a morning! I was not even given the courtesy of a rejection letter or phone call after traveling two-thousand miles on my nickel for this interview.
My FSI interview took place over four days (!). I recall that Thursday involved taking three writtens that were really copped from the ASA books and a very easy BAI sim. Friday was a flight with an Assistant Chief Pilot and an interview with the Center Manager. After the flight, I rushed over to the local cleaners to have my suit cleaned in preparation for my Sunday interview with the Chief Pilot. There was nothing on Saturday. On Sunday, the Chief Pilot basically explained that they were looking for "senior instructors" to teach in their contract programs. Then, he offered me the job. FSI put me up in one of the VIP bungaloes on the main campus, which impressed the hell out me. I was also impressed that the interview was a four-day process. It just seemed professional.
I worked briefly for IASCO in Napa, California. I was warned that this was an extremely formidable company, which I certainly learned later. Interview was with the Chief Flight Instructor, after which I was introduced to the Japan Air Lines captains on site. I was told before the interview that there would be no sim or flight, but I was given a sim anyway. They said they "had just started doing it." It was a one-day affair.
Same for Mesa. Mesa indeed provides space-available non-rev travel from a city it serves to Farmington. I paid my way from Sacramento to ABQ, and waited all day for room on an FMN flight. Good thing I arrived two days early. Interview was with the Chief Instructor and corporate counsel. Very easy interview with general questions. No technical interview or written. I understand that has changed, and that MAPD applicants must take a written. I then when on a flight in a Bonanza, to shoot the ILS 25 to FMN. Now, I understand they give a sim.
Finally, I worked at Arnautical Training Center in a contract program. I had already spoken several times with the operations manager before the interview. It was a two-hour morning affair with the manager and the three United captains who owned the place. No flight, sim or written.
As you can see, CFI interviews run the gamut. I felt my FSI interview was far more thorough than any airline interview I attended. My best $0.02 advice is to be prepared. I would approach it as an airline interview. Try to find out beforehand if you will be taking any written exams and/or sims or flights, and hone your skills for them. Study as hard as you can for the writtens because good scores will pay off. You should learn as much as you can about the company. Prepare for a technical interview. Of course, be candid with your answers. Anything less than that will come off as being disingenuous.
Hope this helps. Good luck with your interview.