With my own acoustic, swapping to bone from plastic didn't change the fundamental character of the guitar but it did make it a slightly better version of the same guitar. I think it depends on the instrument. Some might benefit, some might not show any difference but saddles are cheap and easy to make so it's always worth experimenting. Buy a handful of bone blanks and keep the original as a reference.
A saddle must have a perfectly flat bottom (or possibly a tiny, 2 degree or so angle to balance string torque). Frets.com has a lot of info on this kind of thing.
Check out Bob Colosi
's site for a wide range of esoteric saddle materials.
Nuts and bridge pins don't matter IMO, although some people might disagree. Differences in bridge pin mass could conceivably have an effect on tone given that low-mass in the vibrating top is a crucial factor in good acoustic tone - a good luthier will weigh out bridge pieces to the gram and is on a constant quest for the lightest, stiffest spruces known to man.