In Angela's computer simulations, the bullet has a perfectly linear trajectory. This is factually impossible, since the longer the distance, the steeper the curve of the bullet fired has to be for the trajectory to compensate for the effect of gravity's down-pull. And the distance here is over one kilometer.
At one point Cam walks into Hodgins' work area where he is running an experiment using caustic drain cleaners to help determine time of death. Cam immediately responds to the fumes in the room, and Hodgins chides her, saying, "Goggles! Goggles!" He then proceeds to hand her a pair of safety glasses (not goggles), which she puts on to protect her eyes from the fumes. Safety glasses do not keep fumes out of the eyes. Both characters would also need to wear respirators or be using a high powered exhaust hood to protect their lungs from caustic fumes - neither of which are visible in the room.
Angela claims that wind does not affect the trajectory of a .338 Lapua Magnum round, since its speed is "three hundred meters per second". Actually, the muzzle velocity varies, depending on conditions and bullet type, from 826 to 1,019 m/s. Nevertheless, she is wrong about windage (the actual term used for wind's effect) - at a distance such as here (1,400 meters), compensating for windage is crucial. A human head is approximately only 150 mm wide and the victim here is hit right in the head.
Dr. Brennan states that Booth holds the record for longest kill, "nearly a kilometer". Kills over a kilometer have been confirmed as far back as at least the American Civil War. At the time of the episode, the longest confirmed kill was was 2,475 meters, 2 and a half times Booth's longest kill.
When Booth confronts James Kent over paying for the death of the Gravedigger, he shows him a cashier's check, and his (Kent's) signature on the front. A cashier's check is signed by a bank employee, not by the person requesting it. By Booth's logic, he should have been interrogating the bank teller, not James Kent.
When Booth points to the bullet hole in the wall then where the victim's head was, he points toward a group of buildings and says that the shooter was "up there." Given the height of the victim, the height of the bullet hole, and that bullets lose altitude over time, the sniper would have been up the street but not "up there" where Booth points..
Booth views an image of a reconstructed bullet and proclaims "That's a .338 Lapua Magnum. But it shouldn't look like that." All he should be able to tell from the picture is the .338 part of that. Even then, at a glance he would probably only be able to tell that it was nominally .30 caliber. That it was a "Lapua Magnum" could only be determined by looking at the case and powder charge, respectively. In addition, if the bullet "shouldn't look like that" how does Booth recognize it?
When Booth and Brennan are in the apartment in which the sniper fired, neither are wearing gloves. While Brennan did use her scarf to open the window, Booth significantly contaminated the crime scene by clearing the table, moving it, and assuming a shooting position upon it, all without wearing gloves. Booth would never make such a mistake.
When Booth finds where the assassin's bullet is lodged in the wall, he traces backward the flight of the bullet in a straight line to where it struck Taffet in the head. Then when Brennan asks where the shooter was, Booth points his hand upward at an angle to a building across the street. An experienced policeman would never assume that a sniper's bullet could travel in a downward angle and then suddenly change direction and move at a horizontal angle.
Heather Tafert tells Sweets that if he testifies at her appeal she will go free. Witnesses do not testify at appeals.