IS THIS A JOKE?! NOTHING was done to fix the netcode.

[Xenobius]

First guess:
One Server handling one player after another, if both Computer have same distance to server and starting to run at same time, the server still have to handle one after the other! So the one who had the luck to be "noticed" faster starts faster too on the screen... The same Computer is not always faster, so that means the difference you actually see can double in worst case!

This one's rather easy, actually.
One of the first algorithms game developers came up with to tackle lag and desync was based on calculated "prediction".
The fact that you can see different player positions on different screens simply means that SE never bothered to implement it, and made a mess of the whole sync.

On a side note, this also means that Chocobo Racing (if ever implemented) will be downright horrid - every other racer will have crossed the finish line at a different time, resulting in endless "I won, but server announced another as a winner" threads.