This weekend I had someone come to our clinic because she wasn't happy with how she was treated at her other vet. She was trying us out, seeing what I and my staff were like. That's not unusual, as I get new clients every day. What surprised me a little was that she wanted to be open about the fact that she was interviewing me, but was also hesitant and embarrassed to say so. I quickly assured her that this was nothing about which to be ashamed, and I always encourage this kind of behavior.
A relationship with your vet is an important one. You want to feel like you can completely trust your pet's doctor. There needs to be comfort in who that vet is, how they will treat you and your family, how they will make decisions, and what their skill level is in various areas. When it comes time to have to make fast decision about your pet's health, you don't want to have to wonder about or second-guess the doctor. Clients also want someone with whom they can have a real relationship over time, letting the vet get to know them and their pet.
Everyone should feel comfortable interviewing a new vet. Recommendations from friends are always good, but you want to check the place out yourself. Make an actual appointment and pay the initial office visit fee. This will give the doctor dedicated time to talk to you, rather than just popping in and hoping someone is available. Ask to see their facilities. As long as everything is clean and there is nothing gross going on, a vet should be very comfortable letting you look behind the scenes. Ask about the experience of the doctors on staff and ask if any have a particular area of interest, or perhaps things they don't do (for example, I don't do orthopedic surgeries). Ask about their hours and the services the clinic offers. Do they do boarding or grooming? Do they take emergencies? Where do you call after hours and do they refer to a local emergency clinic? Do they have specialists they refer people to? Who can you talk to if there are any problems at the clinic? Above all, just get a feel for the vet and who they are as a person. In the end it's all about your trust level in that person.
You don't have to reserve these questions for a vet you're just starting to see. It's also appropriate to ask things like this to a vet you've been seeing for a while. If a vet isn't willing or able to adequately answer these questions, a red flag should go up in your mind. You should never be made to feel that questions like the ones above are inappropriate.