Automatic weapons are already banned here.
No, they are not. They should be, though. Assault rifles are banned, and that term has a very clear definition.
Automatic weapons and silencers are used very infrequently in crimes. The machine gun act of 1986 plays a part in this.
Also assault rifles made before 1986 are not banned if they have the paper work.
If the current system for acquiring small arms followed the same steps as when you try to get an automatic weapon before 1986, I think that would help alot.
However, as junker said, I can't think of a good system for keeping nuts away from guns. There are some things I can think of, but no system is perfect and people will fall between the cracks or buy them illegally.
I wouldn't feel bad about making it illegal to sell guns privately or passing them.
Also, as scg said, there are rednecks and other people who would be quite dangerous. I am sure she knows some in Florida first hand as I do in Texas.