If you are refinancing from one ARM to another, check the initial rate and the fully-indexed rate. Also ask about the rate adjustments you might face over the term of the loan.
There are literally thousands of mortgage companies all over the country. It is important that you choose a reputable one. Most reputable companies will be part of the Better Business Bureau or other community watchdog group. Good companies will also have websites that rank well on search engines such as Yahoo and Google.
Weigh the costs carefully of how long you will be staying in your home vs. how much of a savings you will be getting in a refinance. Make sure you include closing costs in your decision.
If there is a big difference between the initial interest rate and the APR listed in the ad, it may mean that there are high fees associated with the loan.