Know your credit score before you begin looking for a loan. If you can, try to remove any blemishes from your credit report before applying for a refinance.
Carefully review the estimated closing costs. If you decide to lock in the rate, the lender will send you a "good faith estimate" of your closing costs within three days. Go over the numbers carefully, and compare them to the ones that appear on the final settlement statement (the HUD-1) from your previous mortgage.
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.)
Unless you are getting a lower interest rate, refinancing your home may cost you more money in the long run and may require you to pay higher monthly payments.