Why were muskets so inaccurate?

Answer 1

It has partly, if not entirely to do with the fact that the musket's projectiles were round and the barrels were not rifled to control the projectile's direction of spin.

Similarly to what happens when a Golf ball gets "hooked" or "sliced", the spinning of the musket ball causes a low air-pressure area on one side, which would push it off course. The pressure gradient across the ball would owe its existence to dynamic pressure q, were q=0.5*rho*v^2, rho is the density of the air, and v is the speed of airflow relative to the surface of the ball. Since different points on the ball would experience different airspeeds due to the combination of rapid spin and forward motion, q would produce the pressure gradient. This is the same idea that allows airplanes to fly, though the mechanism which produces the gradient is different.

There would be no way to adjust for this effect since the projectile would spin differently each time the gun were fired, thus the notorious inaccuracy of old time firearms. (Note: This effect only exists when the ball's axis of spin is not parallel to its direction of travel; this is why modern riffled firearms are much more accurate)