Set-ups:
1 400MHz G4 Ti Powerbook, combo drive; OS9.1; Apple DVD Player vZ-2.5
2 800MHz G4 15" iMac, superdrive; OS9.2.2; Apple DVD Player vZ-2.7
3 800MHz G4 15" iMac, superdrive; OSX 10.1.5; Apple DVD Player v 3.0.1

DVD 1 Buena Vista Social club
DVD 2 Little Shop of Horrors (A classic, trust me!)

DVD 1 plays fine on all 3 set-ups.
DVD 2 plays fine on set-up 3, but never seems to load up on set-ups 1 or 2.
Inserting the disc starts Apple DVD Player which shows "loading" and stays
there.

Any ideas as to what the problem is. Since set-ups 2 & 3 are the same
hardware, the problem must be software-based?

Not necessarily. Various DVD drives may read 'marginal' DVD's with varying degrees of ability (especially dual layer DVD's). I've got DVD's that play fine on a DVD player or an iMac but not at all on a PowerBook. You might also want to use Apple System Profiler and see if both machines 2 and 3 have the same DVD drive in them, and the same revision of the firmware.

I notice that DVD 1 (plays on all) is 16:9 Aspect ratio whereas DVD 2 (plays
only on 3) is 4:3 aspect ratio - I would have thought that all the Apple DVD
Player versions would have automatically adjusted for that? or does it have
to be set manually somewhere on the older versions.

AFAIK, If the aspect ratio of the original is 4:3 there's not much point in displaying it in 16:9 unless you want to distort the image.

Have fun,
Shay