not at all gun shows or , that's one of the problems. there is also no background check required with a person to person gun sale you are only "required" to fill out an ATF form 4473 and keep it. the form only states that the buyer states him/her are legally allowed to purchase a firearm and are not prohibited. so basically the honor system.
since I've been in FL for 4 months i've been to about 5 gun shows and had a background check at each one. but these were guys selling guns mostly likely out of a brick & motor building somewhere.
is it a "huge" problem, probably not.