Ask the lender or broker for a comparison of the up-front costs, principal, rate, and payments with and without this rate trade-off.
There is a refinancing myth that says you should not refinance your mortgage unless your interest rate will be at least two points less. This myth is not necessarily true if there are other benefits to the refinance or other reasons behind it.
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.
Ask the company carrying your current title insurance policy what it would cost to reissue the policy for a new loan. This may reduce your cost.