I wouldn't discount the Coriolis Effect on rocket launches or other, military-grade ballistic weapons. It's just not something I would consider for any sort of civilian weapon I would consider firing.
Newtons laws (which is how we predict motion) apply in an inertial frame. The Earth is a rotating frame, so unless you convert everything to an inertial frame first, you have to account for the motion of the rotating frame (Coriolis, centripetal, and centrifugal accelerations).
For rockets, we usually make the conversion to inertial coordinates and just use straight Newtons laws. But for short range applications like shooting, the rotational effects of the Earth can often be ignored. They are there but third order effects. And the non-engineer laymen likes to think of the Earth frame he is in as an inertial frame for his practical purposes, though its really not.
I have only a little experience out beyond 1000 yards shooting. For anything inside 1000 yards, Coriolis effect is an order of magnitude below other effects, like spin drift, so it can pretty much be ignored. As others have said here, beyond 1000 yards, or when the loft of the projectile keeps it in the air for several seconds or more, then Coriolis might become significant.