In addition to what was mentioned, I asked how they handle discipline. Do they have a discipline system, what is it, how does it work, etc. This could be different over there, but over here, I found this was a very differing thing with how they handled it, and some places I liked, and others I didn't like their methods so it was an automatic no for me. Actually, the preschool that my younger son goes to right now, I don't particularly care for the discipline system, but don't have another option because we moved to such a small town that this is the only preschool option we have. They take away outside play time as disciplinary action, which I feel is important time for them to have when they are just little kids. There are so many other things they could do rather than that, so its kind of frustrating.
Also, what type of teaching method do they use? Is it more play-based, or more set up to introduce them to what they will transition to in kindergarten?
What does a typical school day look like? What is the general rotation of activities, just to give you a feel for what types of things your child will be doing, and getting out of the class.
Do they provide a snack, does the parent provide the snack, or does the parent provide a classroom snack on a rotation basis? If it's a full day thing, what about meals?