The few people I know of who were stopped at an NICS check had a misdemeanor drug conviction decades before or had something sealed/expunged they thought wouldn't come up and it did.
In all cases, they hired a lawyer to "fix it" and were approved in 6 months.
As long as militaries in the third world have millions of firearms they will be available in the first world for a reasonable price, especially to criminal organizations. Anyone who has done even a cursory investigation of arms trafficking knows this fact.
Al makes a very good point also.