Q:

I was also trying to understand the Input-reference differential voltage of 40V. Does this mean that the max voltage between the input and output can be 40V? (Ex: If I used +72Vdc at the input, I will only be able to get  +32Vdc at the output ?).

A:

Yes, the 40V absolute maximum rating of the LM317 means that if Vin goes more than 40V above Vout, the IC could be damaged.  The output voltage setpoint is maintained by the voltage set at the ADJ pin.  So, if Vin is raised past 40V above Vin, then the IC will still maintain 12V at the output--until it breaks.  i.e. the IC will not increase Vout to maintain 40V across itself.

TI just released a 100V tolerant LDO--the TPS7A4001.

Lastly, understand that power dissipation of the LDO is equal to (Vin-Vout)*Iout.  So, at very high input voltages, the LDO will have a very high power dissipation that must be dealt with.