When 24V is applied across +I and -I what is the voltage drop across the LM317?

So, you haven't built up a test circuit containing LM317 to test the performance of this current limiter? Joe, it's extreaordinary necessary to INTENSIVELY test such a design by yourself. You must get a feeling how it works. There are many details, which cannot be caluclated into total detail. Don't trust too much these calculations. Even if calculations make you feel everything is alright, it can be just the opposite, because you might have overlooked something!!!

Now to your question:
If 24V is applied across '+I' and '-I' inputs, then current limiting action is invoked. Assuming that 1.25V / 51Ohm = 24.5mA is flowing, this gives a voltage drop of 2.45V across shunt resistor of 100Ohm. About 1V is dropping across LL4148, and 1.25V is dropping across 51R resistor. The rest, namley 24V - 2.45V - 1V - 1.25V = 19.3V, is dropping across LM317, of course. Where else???
So, a heat of 19.3V x 24.5mA = 0.47W must be dissipated via package. And it's the best idea, to use TO-263 package in combination with large enough copper plane of PCB. Keep in mind, that your circuitry is coated by some material, which means, that heat transfer can be highly degraded. So, use this TO-263 package in combination with comfotably large copper area.

With the 2.5V drop across the the LM317 how does that effect the compliant voltage of the current sources? If the voltage sources are specified at +12 - 28 does that mean that +15 should be the minimum voltage when using the LM317?

Compliance voltage is the voltage drop across shunt resistor caused by the signal current (4...20mA). If you want a current source to be able to drive 500R shunt resistance, than current source must deliver a minimum compliance voltage of 20mA x 500Ohm = 10V.
If one's current source is some kind of exotic and does only provide a mimimum compliance voltage of 5V, then maximum shunt resistance is 5V / 20mA = 250Ohm, assuming that there are no other voltage drops.
In your application current source must deliver a minimum compliance voltage of 5.5V with 100R shunt resistor. 5.5V is the sum of voltage drops across shunt resistor, diode, 51R resistor and LM317. This is normaly not a problem, but who knows...

The 30V transorb on the +I, -I is it's purpose to block out any short duration voltage spikes that could damage the LM317?

Exact!

Finally can you explain the operation of diodes LL101A and LL4148 around the 89C52?

The according circuit is a simple passive level shifter. Of course, you can also use a more sophisticated circuit.
You might ask, why not just using two identical resistors, and omitting these diodes?
In order to achieve not too slow switching, output of TLC352 should be driven rather low impedantly. There's also some uncertainty about the absolute height of output low voltage, so that it may become difficult to produce stable and secure logical low voltage at input of 89C52.
This circuit circumvents these problems. Resistors are chosen so differently, that Schottky diode LL101A is surely forward biased. This gives a stable and well known potential. LL4148 is needed to insure that potential at input of 89C51 is not becoming negative.

Kai