Yet problems seem to persist. Last summer Alexandra Penfold and her husband decided to refinance their New York City apartment. Though the home is a legal two-bedroom, the appraiser recorded it as a one-bedroom. Even though a similar two-bedroom in the building had just sold for $25,000 more than Ms. Penfold and her husband had paid for their apartment in 2008, the appraisal came back shockingly low — $110,000 less than their original purchase price.

Ms. Penfold notified the bank of the mistake and sent a copy of the offering plan to prove that her apartment had two legal bedrooms. The bank never responded, and she eventually refinanced with another lender.

After researching Ms. Penfold’s refinance application, Amy Bonitatibus, a spokeswoman for the bank, JPMorgan Chase, said, “We fell short in serving this customer and are refunding her fees.”  

The best way to challenge an appraisal is to provide evidence as to why it is wrong, be the evidence an offering plan or relevant comps. But that can be an uphill battle. “You have a better chance of winning Powerball than getting a lender to abandon the first appraisal,” Mr. Miller said.