The next two paragraphs are all background information. If you want the American Sniper content only, skip them.
I recently wrote two posts on movie mistakes. I haven’t seen all of American Sniper yet. Nor have I ever trained as a sniper. First, LE snipers, from S.W.A.T. to F.B.I., don’t train the way military snipers do. This is mostly because LE snipers deal with one kind of situation: hostage situations. When they are called in, they take up a position fairly close to the building (or area, structure, etc.) in which at least one individual is located whom they may have to shoot. By fairly close, I mean in general from 50-150m. That’s why police sniper rifles often use 5.56/.223 rounds, whereas military snipers almost never do, and why police snipers need rifles capable of incredible accuracy that simply isn’t possible with any rifle over long ranges. It’s true that some military snipers are required to deal with the same type of situations, particularly elite, anti-terrorist units like 1st SFOD-D/Delta Force, SEAL team 6 (DEVGRU), and probably groups that we will learn about later as we did with ISA. However, in general (and even in the case of SEAL team 6 snipers), the training is more general and the rifles almost all have rounds at least as powerful as the 7.62 NATO rounds.
Second, while both LE & military snipers do receive training from private facilities (such as courses on firing from aircraft, boats, etc.), even most LE/military personnel can’t take these courses. In general, the closest that most can get to such training are long range rifle courses, which luckily are too expensive for many as they are essentially courses on how to be an amateur sniper that anybody can take, and most shouldn’t (in my opinion).
However, one of my instructors in a week-long course on tactical shooting (carbine/pistol) was an ex-SEAL team sniper. I remember that, at one point, he was demonstrating something in the prone position and another instructor (ex-Arizona SWAT) pointed out that the prone ex-SEAL had his feet turned such that the inner side of each foot was pressed against the ground. This is important for snipers because 1) they spend a lot of time in the prone position and 2) they want to minimize the area they present to a potential counter-sniper or even an unarmed spotter.
There is a scene in the movie after which the main character has finished BUD/S (basic underwater demolition/SEAL training), and is being trained as a sniper. The instructor is walking past all the students, each one prone with a rifle and firing at targets downrange. In a portion of this already short scene, and while the instructor is giving a kind of “speech”, without missing a beat in the speech he uses one of his feet to “flatten” one the foot of one of the students (i.e., step down on the student’s heel at an angle so as to push the foot such that the inside of the foot is flat against the ground). The ex-SEAL team 6 sniper I knew fired with his feet like this even when using a carbine. It’s a tiny detail that almost nobody would catch or understand, but which is absolutely authentic.