Both seller and buyer agreed to a purchase price with all the details agreed upon. The financing was not an issue either. The only issue that created a problem was the difference in the square footage. My home appraisal from 2015 listed the property for 300 square feet more than the current appraisal. This has resulted in my appraisal coming in $15K less than needed. I actually agree with the new square footage #, and want to see if the previous appraiser can be held liable for misrepresenting the square footage to me. Can I sue the appraiser for the egregious error?
To be able to sue the appraiser, he would have to have a duty to you. If he was hired by a bank, his duty is to the bank and not to you. Assuming that you directly hired the appraiser, then you would have to check the contract for limits on his liability – a clause that says "you waive your right to sue me for (certain) mistakes". Now supposing that you haven't waived your right to sue, you almost certainly cannot sue for misrepresentation, unless for some reason you can prove that he knew that he was lying to you.
Your best bet is arguing that his mistake was negligent. You would have to establish that the first figure was incorrect (a disagreement in figures does not establish which figure is correct). A discrepancy between county records and an appraiser's estimate can be explained by numerous non-negligence related facts (unpermitted modifications of the structure, for example). Suppose that the source of the discrepancy is inclusion of finished basement space in the earlier appraisal, or perhaps measurement error. Then you would have to prove that that error involved a lack of professional care, which implies certain professional standards (not just your feeling that the error is egregious). This article explains the ANSI guidelines. The standard tends to increase square footage because it is measured from the outside.
Then you would have to establish that you were damaged by the earlier figure. The law doesn't allow you to sue because someone does something that bugs you, you have to have suffered damage. You don't say how you were harmed – I presume the problem is that the buyer's bank is not willing to lend that much money, where you relied on an earlier incorrect estimate of square footage in advertising the house and setting the price. You may have contributed to the problem by relying on that estimate when you knew or should have known from the government records that the size is something less. There is some possibility of legal recourse, but it's not obvious (so gather all of your facts and talk to your attorney).