I'm not a deep-in-the-weeds expert, but if I had to put together an "obvious long rifle mistakes in fiction" article, it’d probably be:
* People pumping shotguns after every round, or unnecessarily cycling the bolt after every round
* Wrong action type for the gun
* Wrong shotgun ammo for the context
* Wrong safety type for the gun (most long guns have safeties, but they are operated in a variety of ways)
* Magazine vs clip vs chamber vs tube
* Shotgun impacts launching people across rooms, or unrealistic recoil (both too high and too low) for the weapon type
Generally, all long guns that are not auto/semi-auto must be cycled after every shot in order to chamber another round. This includes pump-action, bolt-action, and lever-action rifles/shotguns. There are exceptions, such as revolver rifles.
There are also instances when semi-auto pistols might need to be cycled after every round.
How about accounting for Coriolis "force" in addition to drop and wind when shooting ULR 5,000 yards?
Have you seen that in a film? Is it actually a thing, can you ignore it?
Buckshot spread is another common mistake in fiction, e.g. when it's close you still need to aim
Many long guns are not semi-auto and have to have their action cycled after each round. that's super common.