Give yourself plenty of time to close. With most refinancings, your file is turned over to a closing or title company, which dictates the closing details. Like the lenders themselves, these firms are swamped when interest rates are low. Moreover, appraisers get backed up and can be difficult to schedule. So don't expect the closing to happen as quickly as anyone promises.
Unless you are getting a lower interest rate, refinancing your home may cost you more money in the long run and may require you to pay higher monthly payments.
When it comes to lowering your rates you will need to weight the benefits of having a lower rate vs. paying points up front. You may end up paying a lot more depending on your choice and how long you plan on keeping your mortgage.
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.