The Thompson isn't accurate at range because the bullet "runs out of powder" or some such crap, as well. Obviously whoever created that abomination of a show hasn't the least grasp of basic ballistics, or of how the guns they're talking about work. Shoddy, shoddy research - IF any was actually done.
Thompson submachineguns are inaccurate at extended range because they fire from an open bolt. When you pull the trigger the bolt flies forward. All that mass rushing forward, stripping a round out of the magazine and then slamming it into the chamber causes imparts quite a bit of motion to the gun. That motion translates into unwanted motion of the muzzle, which means the bullet isn't aimed remotely close to where the sights were when you pulled the trigger. FYI the .45ACP is quite accurate out to 150 yards or better when fired from a carbine length barrel.
I could nitpick that show to pieces, but it would take too long. There was just so much outright wrong info, and so much more that was misrepresented, that it would take a not-so-small book to correct it all.
Note to show's producers: Study basic physics, then get some real firearms experts, those who understand the basic principles of how firearms and ammunition really work, then try again.
To support your postion
The prove that pistols and pistol cartridges can be useful at long ranges with the right modification
This thing was used in WWI by arty soldiers to defend themselves on guess what ... long ranges.
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