One of the most important questions a parent can ask a prospective tutor is "How many years have you been tutoring this subject?".
Tutors who have been teaching a subject for years, who have taught it in a classroom, such as I have, and have taught their subject, such as Chemistry on the AP level as I do, separates a college prep or college-level instructor from an after-school tutor.
Another great question to ask is "do you offer an intensive study course?"
The best way to learn a subject is to cram a year's worth of classwork into 6 weeks of study. Over and over my students have experienced amazing success in taking a home school course or an AP study course in 6 sessions and raised their achievement by 2-3 grade levels. I have worked with many D students that hit the high B's to an A, by making Chemistry simpler, easier, and better understood.
Chemistry and mathematics, like Geometry and Algebra are not too difficult to be conquered by any student. Often times, its that the class and teacher left the student behind, and didn't do a good enough job explaining the subject matter. When it is presented in a clear an simple manner any student can learn it!
I love teaching, and every time I see that light bulb go off in a student's head it is a truly amazing thing to witness.