If you think your Govt. is efficient enough to sift through 423 million form 4473s...to find you....you have more faith in them than I do.
They are very efficient if the IRS is any indication. Leave out a 1099 form for $600 when you fill out your tax or accidently put one digit of an SSN wrong on a 1099 you give a contractor. I've done both and was caught both times.
As to illegal weapons I was told straight up by an assistant U.S. Attorney not to bother with a case of a felon with a firearm. They didn't have the resources to pursue that. Almost a guarantee they will find time and resources to make an example of "hoarders" with "arsenals". That would be someone with 10 guns and 1000 rounds of ammo.