Why a diode to GND in 0-30V LM317 circuit?
There is a reason to put the diode there--- it keeps (much) current from flowing in reverse through the output load to the negative source because the diode becomes forward biased in parallel with the regulator parasitic diode, so the LM317 output never goes very far below zero even if the pot is set all the way down in resistance. 

The main issue with it is that the voltage stability is directly dependent on the -10V source. A 1% change in the -10V source represents a 10% change in a 1.00V output voltage. 

I prefer variations on the original NatSemi circuit here: 



The 1.2V shunt regulator in conjunction with the -10V source and 680R resistor creates a stable negative reference that allows the adjustment to go down close to 0V. You could use an LMV431 (rather than the obsolete LM113) which is much cheaper and better matched to the LM317 (1.24V). 

Note that in both cases, if the negative voltage is not present at the time the regulator powers up, the regulator output can exceed the set voltage- by as much as +10V (or more, depending on whether the source can be pulled positive) in the OP's circuit and by +1.24V to about 2.0V in the circuit above.