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.
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.
Close inactive credit card accounts to improve your credit score, making you eligible for lower interest rate loans. You will need to notify the credit card companies in writing that you wish the accounts closed on your request. Next, check your credit report after 30 days to be sure closed accounts include the comment "Closed at Customer's Request." You want future lenders to know it was your request and not bad credit that closed your accounts. Also, take the time to check for any mistakes in your credit report that could negatively impact your credit score.
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.