In contrast with vet school interviews, where the questions can be all over the place, the questions for faculty interviews are usually pretty similar. Here are the important ones I can think of.
“Why do you want to work here?” This is almost always asked during an interview, often repeatedly by a variety of people. “Because they will pay me” is clearly an unacceptable answer. Find something interesting about the institution. I myself am not a fan of personal reasons like “Because my family is here.” I prefer professional reasons like, “I hear people enjoy going to work here and I like working with positive people” and “I want to build a program, which is what you are looking for someone to do here” and “I can pursue the research which is interesting and productive for me here.” Obviously, personalize your answer and have it be more than one line. Never ever say, “Because the place I am now is horrible.” Even if this is true, no one wants to hire a new faculty who is running away from something, they want to hire someone who is running towards something.
“What research do you want to do?” Academia is about teaching, research, and service. Unless you are applying for a strongly clinical position with no expectations for research, you will probably be asked this. Even if you are going for a strongly clinical position, have an answer ready. It will be a check in the positive column for you. For tenure-track positions, they may want to know about your prospects for grants or a direction for your research. Your answer doesn’t need to be a multi-page proposal, but you should have a few decent ideas.
“What would you want to change if you came here?” This may be asked specifically regarding clinical services. Hopefully, you know enough about the service to answer, but if you don’t, it is perfectly fair to give a general answer or explain how you typically approach problems with the structure of a service.
“What do you want to teach?” I admit I’m not sure if I’ve been asked this, but I think it’s a fair question and I am always prepared to answer it. You’ll probably be expected to contribute to the core class(es) taught by your discipline, but if you are excited to do an elective, you could mention it as well.
“Why should we hire you?” It probably won’t come out like this, but that is the sentiment. You may be given an opportunity to explain why you are the best candidate for the position. As always, be humble, but you can take the opportunity here to explain what you feel you bring to the program. The “You-Do; I-Do” model is a great way to convey this information without sounding like you’re bragging. If you are excited about bringing clinical research, but they want a benchtop scientist, then it’s better to figure that out now than after you start! Again, as always, be honest.
Those are the questions I can think of which are common to faculty interviews. Obviously, many other things will come up over the course of a one to two-day interview. But if you prepare for these questions (and their variations), I think you will have a good foundation for an interview.