If you are planning to stay in your home for several years, then you can save money by paying points for lower interest rates. You pay up front fees to ensure you have lower interest payments over the course of your loan. Remember, this only works if you keep your mortgage for several months.
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.
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.
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.