Their attitude to self diagnosis is a good one to check. Also:
How do they filter for an adult person masking, or having learnt skills as an adult that they didn't have as a child?
Do you need to provide testimony from your family / your parents, and how do they handle family dinamics such as a parent who is unwilling or unable to recognise autistic traits?
Do they only provide you with the diagnosis for Autism, or does your evaluation include more detailed feedback such as what co morbidities / challenges / sensitivities you have?
How aware are they of gender-based bias in assessing autism?