First of all, make sure you are working with or can speak with the person who will actually make the decision about hiring you.
Find out if the budget has already been approved. If not, when and how will that approval decision be made.
Determine, as best you can, if the company is solvent and will be able to pay you. (You can't really ask this; you will have to discern it). If you know other contractors who have worked for this company recently, ask them how quickly their invoices got paid.
Look for credit information on the web or in the library. Try www.hooversonline.com and Dun and Bradstreet Reports to determine how on time they are with their other business bills.