If you are refinancing from one ARM to another, check the initial rate and the fully-indexed rate. Also ask about the rate adjustments you might face over the term of the loan.
If you are making payments on a long term loan, say, 30 year mortgage for the past 10 to 20 years, then refinancing to another 30 year loan will not be a good option as it may increase your overall payment.
Calculate the financial benefit of refinancing in one, two, or three years. Does the benefit compare with your plans for staying in your home?
Make sure that your original mortgage does not have a pre-payment penalty or early payoff penalty of any kind. Sometimes people will get into their mortgage with the mortgage having a pre-payment penalty and they will not even know about it. Pre-payment penalties usually range from 6 months to 3 years with a penalty for an early payoff. The penalty is usually about the amount of 6 months worth of your mortgage loan interest, but this varies. You would have to be able to have some significant payment and interest savings on your refinance loan to justify refinancing a mortgage loan with a pre-payment penalty.