It is said that Cobb purchased the rifle with a prepaid credit card. In the security camera footage of him buying the rifle, it shows him counting out cash.
When Cobb is making his bed in his cell, the folding table in front of the toilet is up. When the camera switches angles when he sits down, the table is folded.
While Ernest is on the hill shooting at people at the carnival he clearly targets the head of the two people on the ferris wheel. Later when Detective Madsen and Dr. Soto are reviewing the crime scene, one of the police officials mentions that all the kill shots targeted the heart.
Detective Madsen speaks with a gun store employee who admits to selling a rifle to a man without a name or address. In actuality the employee would likely have been arrested and the store investigated as it is illegal to sell a firearm to anyone without at the very least a name and address so that a background check can be performed.
It is stated that Cobb uses a Winchester Model 70, though he is shown assembling a rifle from two pieces. There is no version of the Model 70 that breaks down into two pieces.
On the roof, just before Hauser shoots Cobb in the hand, a gun cocking sound is heard. His gun is a hammerless model incapable of making that sound. This sound is also usually heard when Madsen pulls or puts away her gun, and is likewise a hammerless model. This sound effect is a common TV firearm error added for dramatic effect.
Cobb is shown obtaining a Winchester model 70 and in a short period of time having a threaded suppressor on the end of the barrel. Doing something of this nature would require the gun barrel being machined to accept the suppressor as well as his obtaining a suppressor. Suppressors unlike bolt action rifles are highly regulated and require special licensing. It is impossible to walk into a gun shop and buy one. He would not have been able to obtain this setup in the time shown, if at all.
The sniper shoots and instantly kills 3 people with center mass shots from a long distance. Using the same rifle and same type of round, he shoots Lucy in the same area of her body from a far shorter distance, yet she survives. Bullets lose energy the further they travel, so a shorter range shot would have more energy and be less survivable.