The first-order approximations are easy. When you start adding up all the other factors, it gets complicated fast. The solar wind, which isn't constant, affects trajectories. Earth's atmosphere is neither homogenous nor perfectly predictable along many dimensions: upper-level wind speeds and directions, air density, and temperatures, to name a few. The Moon's gravitational field is very lumpy. Earth's gravitational field, while relatively smooth compared to the Moon, also isn't perfectly uniform. Propulsion systems have tolerances. Same with parachutes. The location of the vehicle's center of gravity affects everything.

All of these factors and more have to be taken into account if you want your predictions to be accurate. Aside from telemetry processing, most of the computing power on the ground during a space mission is used for churning out navigation solutions.

Agreed.

Fun info: The NASA orbital codes include things like photon pressure... from sunlight reflected off of other planets in the solar system. At some point, I think they are just showing off :)

Not a great analogy because there actually is interference and golf balls aren't typically monitored and course corrected during flight