Regarding private sales, I'd really like a system whereby the buyer can generate a 1-time code (by filling out some information on a gov't website, for instance) that's good for say a month. The seller can then enter that code, see that "John Smith" is clear to buy a gun, and after checking the buyer's photo ID can sell him the gun in relative confidence that he's not selling to a prohibited possessor.

This would help eliminate private party sales to prohibited possessors, but it has the unfortunate (to gun control advocates) of making firearm sales more convenient and safe; their desired solution is of course to eliminate private sales.