I've addressed the difference between market value and contract prices before. Suffice it to say, one crazy offer does not equal a market. In the last two years I've seen two properties personally that received over 40 offers. In another instance of only 5 offers, a buyer offer $100,000 cash over every other offer... they won't see that money again for years.
So, what do you do when the market value (this is what an appraiser has the state and federal authority to determine for a home) is different than the contract price (what two people have agree to exchange).
Read the report - this should go without saying. When I receive a call from the buyer/seller's agent, this is my first question - Did you read my report? 50% of the time, they haven't received a copy. 25% of the time they've read it. Even if you disagree with "the number" read how the number was developed. This is a great opportunity for you to discover possible mistakes that the appraiser has made and needs to fix which might effect value OR you may come to understand how they came to that market value opinion.
Look for errors in the report, that matter - I once had a reconsideration of value and an error that was noted was for a street direction. I had typed "S" instead of "N," which I happily fixed, however, this is pretty deep in the weeds to include in a request to change the value. Confirm the living area, bedroom and bathroom count, and other major features (I've missed a half bath before and had to go back out and take pictures and redevelop the value opinion).
Look at the comparables used - 99% of the determination of value is in good comparables. If I have good "comps" I can write a great report. If I have limited, horrible comps, its going to be an ugly report - that doesn't mean it will be "wrong" just far far more difficult. If you have better comparables, state why they are better and provide them.
Understand that buyers bringing cash to the table is how a healthy market increases - Your sale today where the buyer brings $10,000 to the table is tomorrow's comparable that supports market values $10,000 higher, but until closing, its just a promise to pay (with numerous escape clauses). The lender doesn't loan on promises, they loan on market data.
For more great information on this subject, read here.