If your property value reduces and you refinance up to 80% of the reappraised value, your original mortgage amount may be higher than this amount. Thus, the new loan will not be sufficient enough to help you pay down the existing one.
Don't fall for the 0% apr unless it fits in with your master plan. A lot of brokers will try to get you locked into a low interest rate that will balloon on you in a couple of years and leave you out on the street.
Be Proactive. Your loan representative should keep in contact with you even if there isn't any action on your loan. But do your part to keep the lines of communication open as well. If you don't hear from your loan representative for a few days, pick up the phone and ask for an update. The old adage that the squeaky wheel gets the grease definitely applies in this situation.
Closing costs can be expensive. If you plan on refinancing your home to save money, be sure to take into consideration how much the closing costs on the new loan will cost you.