If your new mortgage rate seems too good to be true then it probably is. Check for hidden fees in your mortgage that will make up that suspicious difference.
You can ask for a copy of your settlement cost papers (the HUD-1 form) one day in advance of your loan closing. This will give you a chance to review the documents and verify the terms.
If your monthly payment on a fixed-rate loan includes escrow amounts for taxes and insurance, your payment each month could change over time due to changes in property taxes, insurance, or community association fees.
When lenders offer a "no-cost" loan, they may include a prepayment penalty to discourage you from refinancing within the first few years of the loan. Ask the lender offering a no-cost loan to explain all the fees and penalties before you agree to these terms.