Once a record is kept, then it is easy if a Feinstein ban on a class of weapons is made, the Government can send you a letter saying "bring in your Daniel Defense AR-15 serial number xxxxx to your local Police Department by xx/xx/xx for disposal. Refusal to comply will result in criminal and civil prosecution."
Me paranoid? You betcha.
In the late 1980's, my college bookstore didn't validate credit cards electronically, but instead checked their numbers against a list of invalid ones. Computer technology is such that if there were a satisfactory solution to the privacy issues surrounding letting anyone know whether anyone else has ever been on the "forbidden list", the issue of proving a check was done wouldn't necessarily be a particular problem. If the seller keeps a copy of the credentials used to purchase the weapon, and there is an indelible public record of who was forbidden on what days, then the fact that the credentials aren't on the forbidden list for the date of purchase would mean the seller was in the clear.
Of course, that wouldn't solve the more fundamental problem which is that there's no reason to believe that the government wouldn't endeavor to add to the forbidden list people who have neither been adjudicated mentally incompetent nor been accused (must less convicted) of having committed any crime. Indeed, only a fool would believe such a thing given the government's effort to do precisely that.