I'm only aware of one case in which someone was turned down, but that was because Disney asked for a larger down payment than typical and the party in question didn't feel like they could do it.
Their loan application is pretty standard stuff: household income, mortgage, outstanding debts. They'll also want a couple of months worth of pay stubs or a tax return if you're self-employed. And they WILL check your credit history with Equifax or another entity.
But, honestly, I think they'll finance virtually ANYONE. They may ask for a larger down payment, or a shorter term, but it tends to be painless. And Disney financing doesn't show up on any credit report (or, at least, that once was the case.)
I will say that we had some junk showing up on our credit report from a crisis period five or six years earlier, but for us it was absolutely painless. No questions were raised, but we did put down a significantly larger down payment than they asked for.