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Refinancing with your current lender without shopping around.
Your current lender may not have the best rates and programs. There is a general misconception that it is easier to work with your current mortgage company. In most cases, your current mortgage company will require the same documentation as other companies. This is because most loans are sold on the secondary market and have to be approved independently. So even if you have been very good at making payments to your existing lender, they will still have to do their verifications all over again.
Not doing a break-even analysis.
Find out what the total cost of the refinance is, then figure out how much you will save every month. Divide the total cost by the monthly savings to get the number of months you will have to stay in the property to break-even on your refinancing costs.

Example: if your refinance costs $2000 and you save $50/month your break-even is 2000/50=40 months. You should refinance if you plan to stay in the house for at least 40 months.

Note: The break-even analysis only works if you are refinancing to save money. If you are refinancing to switch from an adjustable to a fixed or from a 30-year loan to a 15-year loan, it is much more difficult to perform a break-even analysis.
Not getting a written good-faith estimate of closing costs.
Your mortgage company is required to provide you with a written good-faith estimate of closing costs within 3 working days of receiving the application.
Paying for an appraisal when you think that the house may appraise too low.
Have the appraisal company do a desk-review appraisal (typically at no charge) to provide you with a range of possible values. Your mortgage company can ask their appraiser to do this for you. Do not waste your money on a full appraisal if you are doubtful about the value of your house.
Using the county tax assessor's value as the market value of your house.
Mortgage companies do not use the county tax assessor's value to determine whether they will make the loan. Instead, they use a market-value appraisal which may be very different from the assessed value.
Signing your loan documents without reviewing them.
Do not sign documents in a hurry. Whenever possible, try to get documents that you will be signing ahead of time so you can review them. It is advisable to ask for a copy of all loan papers you will be signing a few days ahead of the close of escrow. This way, you can review them and get your questions answered. Do not expect to read all the documents during the closing. There is rarely ever enough time to do that.
Not providing documents to your mortgage company in a timely manner.
When your mortgage company asks you for additional paperwork, jump on it! Do not complain. They are trying to get you approved, not trying to hassle you unnecessarily! Jump through the hoops as quickly as possible. Borrowers who do not respond to requests for documentation quickly enough can end up paying higher rates if their rate lock expires.
Not getting a rate lock in writing.
When a mortgage company tells you they have locked your rate, get a written statement which details the interest rate, the length of the rate lock and details about the program.
Pulling cash out of your credit line before you refinance your first mortgage.
Many lenders have "cash-out" seasoning requirements. This means that if you pull cash out of your credit line for anything other than home improvements, they will consider the refinance to be a "cash-out" refinance. This leads to much stricter requirements and can, in some cases, break the deal!
Getting a second mortgage before you refinance your first mortgage.
Many mortgage companies look at the combined loan amounts (i.e. the first loan plus the second) even when they are refinancing the first mortgage. If you plan on refinancing your first, check with your mortgage company to see if having a second will cause your refinance to get turned down.

Refinancing Your Home - Top Ten Mistakes