The "gun show loop hole" absolutely needs to be closed. Some licensed gun dealers do sell at them, and do back ground checks on the spot. They can phone them in. You run into problems with private dealers. A person from *insert state here* can sell to another person from *exact same state* without any checks. There are a few other little cracks.
The background checks are pretty thorough. They check several record systems, but again, you have the legal loop holes.
*A longer waiting period and perhaps more personal checks (speak with family or...) would be a good addition. That would not always be ideal (people lie) either, but... It might be helpful.