I don't believe that it is safe to be selling firearms to people over the internet. It is too easy to steal someone's identity and them purchase a firearm under their name. At least in the store you are actually present when you are purchasing the weapon, so it is safer than selling it over the internet.
People sell their guns on private sites. As of now, there is no requirement for a background check to purchase a gun online. There are sites that function as "flea markets" online and under the anonymity of the Internet, allows unlicensed sellers to advertise weapons. Felons then see them and purchase them. However, the Senate is trying to pass a law to rectify this problem.
Anyone who says there is an online loophole for gun buyers needs to honestly try to buy a gun online. All the online dealers make sure your gun get's sent to a federal dealer where they will preform the background check. Seriously. There is no loophole. These lies are ridiculous.
Buying guns online is not a "loophole" or "easy" compared to buying a gun in a brick and mortar store. Federal law prohibits the interstate shipment of firearms except between Federal Firearms Licensees (FFLs), more commonly known as gun dealers.
If one wishes to purchase a firearm from an online retailer (an FFL), the firearm must be shipped to another FFL (specified by the customer) and must meet the laws of the state where the customer resides. When the firearm arrives, the customer must pay a transfer fee, background check fee, and undergo a background check the same as if he'd purchased the firearm from a brick and mortar store.
If one wishes to purchase a firearm from an individual online, the seller must take the firearm to an FFL who will then ship it to the customer's FFL and the same fees and checks stated above are still applied.