When it was allowed, appraisers used to stretch values to please mortgage reps and realtors, in order to get deals approved and gain their future business. That is a big part of the reason home prices were so artificially inflated back in 2005 and 2006, so it had to be stopped.
The only way I know of to maximize value is to look up comparable sales within 1/2 mile and check and make sure your appraiser chose the correct comparables in his report. If you find better comps, or newer sales, then definitely let the appraiser know about it (assuming they are true comparables), that used to work for me.
Best and cheapest way to find out the potential value of your home before hand is to have a realtor do a CMA (Comprehensive Market Analysis). Although not an actual appraisal, if its done correctly, it can give you a fairly accurate expectation of what your home will actually appraise for. If you know any realtors, I would ask one to do a CMA for you. Its done via the internet, should take no more than 5 -10 minutes, and should cost you nothing (unless you're going to treat them to lunch) to do. Good luck.
There are sevral ways to address this. a) You can hire an appraiser and get an appraisal on the home. b) Call me and I can send you comps of recently sold homes so you know the home values in your area. An appraisal or comps will give you an idea of fair market value of your home.