Ask who will actually teach the lessons, and whether it is the same person every week. Continuity matters more than credentials in this subject, because a teacher who has heard you read for three months knows which of your mistakes are habits and which were one-offs.
Ask how a student is assessed at the start. An academy that places you by a short read-aloud is paying attention to where you are. One that places you by age, or by asking which book you own, is guessing.
Ask what happens when a lesson is missed, on either side. The answer tells you whether there is a real schedule behind the offer or an availability calendar that shifts every week.
Ask how progress is reported and how often. You want to know what was covered and what is next, in enough detail that you could verify it yourself. Vague reassurance is not reporting.
Ask about the teacher's own training in tajweed specifically, not just their memorisation. These are different qualifications, and the second does not imply the first. A hafiz who has not studied tajweed formally may recite beautifully and still be unable to explain why your madd is short.
Then ask about fees, timings and what a trial involves — and get those in writing rather than from a marketing page, because they are the details most likely to differ from whatever is published. If you would like ours, the admission form is the quickest way to reach a person who can answer for your situation, and the contact page has the alternatives.