As for education: Same as Skittles...in a former life, I reviewed the appraisal reports, too. My job was not to agree or disagree with the value but to make sure that the appraiser got there correctly. Did the appraiser inspect the place, what data did he collect and use, was there enough data used, how were adjustments made and why, were all of the calculations done correctly?
I stayed current on banking guidelines and USPAP. There was some continuing ed that was offered (I'm thinking it was from appraisers?) on reviewing sales and income approach that was very helpful, especially for the larger, more complex commercial appraisals.
As for disputes: Once I said yes to the report and forwarded it to lending - - -that was it. The only times I remember getting any push back were those similar to Randy's square footage above. Once, I matched the property to the engagement letter and the appraiser matched to the county records - - turns out both of us were supposed to magically know that the borrower was offering the bare lot adjacent to the home as well.
If the appraisal was done correctly and the borrower doesn't agree with the results, they should be able to point to something specific, yes? My lot is bigger; he missed a bathroom; that's a 3-car garage, etc. Then that is something that can be taken back to the appraiser for review and possible revision.
Hope that helps some. I can look for where I got that training. It will be dated, but might be a start.