Don't fall for the 0% apr unless it fits in with your master plan. A lot of brokers will try to get you locked into a low interest rate that will balloon on you in a couple of years and leave you out on the street.
When evaluating different lender offers, in the mortgage loan pre-approval process, pay closest attention to the interest rates they are offering & the closing costs. These are the two biggest factors that will help you figure out which lender is right for you. If one of these two factors is too high, it could offset the benefit of refinancing for you.
You have a legal right to a good faith estimate. Get a copy of this document and go over it with a fine tooth comb, it will reveal where there is a real problem.
If you have bad credit, find a lender who is willing to work with you and offer you reasonable loan terms.