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 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.
Ask for more than just rates. Bad loan officers will tell you anything to keep you on the phone -- then change the details to suit them later. Instead, make them get real with you! Ask how long they've been in the industry. Probe them about their experience in the industry. Also, ask what their opinion is on the current market and where it's going.
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.