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.
Know your credit score before you begin looking for a loan. If you can, try to remove any blemishes from your credit report before applying for a refinance.
When refinancing, don't take the first offer that comes around. Instead you should actively compare both interest rates and lenders.
If you plan on moving out of your existing home within the next few years, it may not be beneficial for you to refinance. Make sure you let your mortgage specialist know your future plans.