Also doesn't take into account the direction of the nap of the cloth on the table - balls rolling 'up' will travel differently from those rolling 'down'.

Would this also mean that the speed of the balls has to be taken into account? The differing effects of friction on the surface would surely alter as the balls move & spin slower?

What about air friction? And the the Coriolis effect? And does observing the balls cause their wave function to collapse? :P

Yes! We demand to know whether the pool table was in the northern or southern hemisphere :)

Tut tut! You're forgetting that the earth is an oblate spheroid, and gravity exerts greater downward force at the poles, than near the equator.

We also need to know the precise latitude of the pool table!

One might as well consider the gravitational gradient exerted by the surrounding terrain and significant celestial bodies, as well as the balls themselves. Should we collaborate on assembling such simulation, taking in account all known physical laws? Or has it been done already? Imagine how cool it would be to toggle different forces or constants and see the result change.

Yes. Friction being constant is a lie that we tell middle school students. In undergrad physics you learn that there is also a linear and quadratic component. That is also a lie since even that assumes perfect balls, etc.