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.
Make sure that your original mortgage does not have a pre-payment penalty or early payoff penalty of any kind. Sometimes people will get into their mortgage with the mortgage having a pre-payment penalty and they will not even know about it. Pre-payment penalties usually range from 6 months to 3 years with a penalty for an early payoff. The penalty is usually about the amount of 6 months worth of your mortgage loan interest, but this varies. You would have to be able to have some significant payment and interest savings on your refinance loan to justify refinancing a mortgage loan with a pre-payment penalty.
If there are only a few years left on your current loan, it's no use refinancing with a long term loan. You may need extra cash but with a long term loan, you'll end up paying more for the entire loan term.
These days most people request a Good Faith Estimate (GFE), but have no clue what to look for on the GFE. Make sure you request a GFE that has ALL fees estimated and disclosed. This includes: origination points, processing, lender, appraisal, title, escrow... ALL FEES... especially the Yield Spread Premium or YSP.