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.
If you are able to get a lower rate that what you currently have, you can save tens of thousands of dollars over the life of your loan. Also, most lenders don't charge as many fees to refinance a mortgage and depending on how much equity you have in your home you may be able to roll the closing costs into your new loan, still have a lower balance than your original loan, a lower rate, and a lower payment.
Refinacing your mortgage can allow you to take cash out of the equity which you have built in your home. You can pay off your higher interest debts and pay all of your debts at a lower interest rate. This will allow you to save money on a monthly basis and achieve your financial security.
You have a legal right to a good faith estimate. Get a copy of this document and go over it with a fine tooth comb, it will reveal where there is a real problem.