This is essential - when I am seeking out a dog trainer, I am not looking for someone to train my dog, I am looking for someone with the knowledge, skills and real life experience that can help me understand my dog, and how to work and problem solve with them.
Certifications and qualifications, testing/assessment- matter, (proof of a formal education), professional associations/affiliations - professional references, continuing education - matter, practical/hands on real life (working with dogs aside from their own dogs) experience matter (a lot) - what training methods and equipment are going to be employed - matter.