If you are planning to stay in your home for several years, then you can save money by paying points for lower interest rates. You pay up front fees to ensure you have lower interest payments over the course of your loan. Remember, this only works if you keep your mortgage for several months.
Mortgage can last a lifetime and that extra 1% can add up to literally thousands of dollars over the years. I have friends that are in their 70s and still paying off their home loans. It'll pay off in the long run to make sure you find the best deal possible. Don't let poor credit stop you from refinancing your home.
Lenders like pristine credit reports. If you have a bunch of open credit card accounts that you never use (and who doesn't?), consider closing them. It will boost your credit score and make you a much more attractive borrower to a lender. Then, a month after you've closed your accounts, go over your credit report with a fine-tooth comb. It should read that the accounts were closed at your request. (You don't want lenders to think someone cut you off and that you're a bad credit risk.)
Short-term mortgages offer lower interest rates than long-term mortgages. You save money by the lower interest rates and shorter payment period. The trade off is a larger monthly payment, but this option can save you thousands.
Pull your credit report from the bureaus and review it for any negative items (late pays, collections etc) and inaccurate detail. Try to dispute negative items and remove them from the report. If required pay off any unpaid debt. Otherwise, you won't get a low rate and may not even qualify. Of course there are lenders in the subprime market who may offer you a bad credit refinance loan, but it's better to avoid them as they'll possible charge higher rates and fees.