Premises liability, in case someone falls on their stupid head and decides it's your fault. Dram shop or the equivalent if yer going to sell alcohol. I had inclement weather insurance, too (but we're outside).
Advertising is a major issue, yes. Me (and anyone I can shanghai) put posters up from here to eternity. I had three radio stations doing spots and I still feel like I didn't cover enough territory. I had some good results last year with a group of us dressing up in garb and haunting public places like Omaha's Old Market. (Watch out about doing this in shopping malls -- they're considered private property, so you need permission, although if yer just shopping in garb, well maybe you can get away with it. I've been in just about every Walmart in this part o the country in me pirate outfit, because whenever I get to faire (I'm a vendor in me spare time) I find that there's a number of things that I need at Walmart. I know of a faire that did well with a "renaissance car wash."
Corporate sponsorship - We just get out there and ask folks. We offer it at various dollar levels, and at each of the levels, the contributor gets a little more bang for his bucks, starting out with free tickets and ending up with tickets, tshirts, banners and so forth displayed near the major attractions (in our case, the joust).
Don't forget ta get yer tax permits and alla that stuff lined up in advance.