SNIP

if there was a shooting and a bullet in good enough shape was recovered it would be easy to connect it with a gun...then the gun with the owner. I see no valid reason why we should not have such a database. If you had proper background checks for ALL gun transactions and a database like this I really think it would solve a lot of problems. I just don't see what harm there is in having such data available to law enforcement. If anything it would sure as hell make solving some of these shootings a bit easier right?

The problem with your logic is where criminals get guns. The law would only apply to those legally purchasing guns:

Where do criminals get guns? Theft, black market transactions, and straw purchases.

In 1985, the Department of Justice reported that only about one in five convicted felons obtained guns through legal channels such as retail stores.5
In 1991, the Bureau of Alcohol, Tobacco and Firearms reported that 37% of armed career criminals obtained firearms from street sales, 34% from criminal acts and associates, 8% from relatives, and only 7% from dealers and 6% from flea markets and gun shows.6
More recently, a Bureau of Justice Statistics survey of state prison inmates convicted of firearm crimes found that 79 percent acquired their firearms from “street/illegal sources” or “friends or family.” This includes theft of firearms, black market purchases of stolen firearms, and straw purchases. The survey also found that 12 percent obtained their firearms from firearm dealers (gun stores, pawn shops), while only 1.7 percent obtained firearms from anyone (dealer or non-dealer) at a gun show or flea market.7
The FBI’s National Crime Information Center stolen firearm file contained over 2 million reports as of March 1995, and an annual average of 232,400 firearms were stolen between 2005 and 2010.8
46.3% of firearms traced by the BATFE in relation to firearm trafficking investigations originate with straw purchasers.9

http://www.nraila.org/news-issues/fact-sheets/2013/private-sales-restrictions-and-gun-registration.aspx
http://www.pbs.org/wgbh/pages/frontline/shows/guns/procon/guns.html

Whether off the street, from an FFL selling illegally, or stolen, they are still obtained illegally and neither the proposed law, nor any database of legally obtained weapons of which those would not be included , would stop that.