Bill cites the United States' lack of background checks for the ease with which he acquired his weapons. This is incorrect for multiple reasons.
Since Bill's weapons are machine guns, they are subject to the FOPA, or The Firearm Owners Protection Act of 1986, which banned the sale and manufacture of machine guns. While fully automatic machine guns can still be purchased by civilians, their ownership is closely monitored and subject to an exhaustive federal background check, federal licensing, and a very steep purchase price (in the tens of thousands of dollars). Additionally, they cannot be sold between private parties without a mandatory federal background check.
There is no possible way Bill could have acquired his weapons legally, which would negate the purpose of a background check.
Gunshots in an enclosed space would not sound like they are depicted in the film. They would sound more like explosions, akin to very loud firecrackers.
When Chip, the TV anchor, returns to the basement where serial killer Bill Williamson is holed up with the broken disk, Bill Williamson refers to the disk as a DVD. It is obviously a CD, as evidenced by its white underside. DVDs have a blue tinted underside.
During the shootout in the TV studio basement, white BBs fired by the SWAT team can be seen bouncing around Bill and the filing cabinet he is hiding behind.
The 5.56x45mm rounds shown being loaded into magazines are clearly dummy rounds, as evidenced by their dented primer.
Bill fires far more rounds than his weapons contain without reloading.
Early scene in Studio 4, Bill's right hand glove exposes his bare thumb. During the interview, the glove is whole.
Although set somewhere in the Washington DC area, a Petro-Canada gas station is glimpsed in the background over Bill's shoulder as he is driving his car towards the TV studio.
A lot of the cars have Canadian license plates when the movie is set in the U.S.
Gunshots are very loud, and carry over a long distance. When Bill is shooting civilians near the bingo hall, people are shown across the street being completely oblivious to the noise.