Making LM78xx fail safe against short, open, reverese bias, flyback, etc
Failure to short- crowbar + fused input (a thyristor and trigger circuit) or at least a TVS. The TVS might be able to limit the voltage to something like 8V which your delicate equipment might have a fighting chance of surviving (newer chips with 5.5V abs max supply may not live). An open GND connection will cause the output voltage to rise so make sure the soldering is solid. 
Failure to open- bad solder connections, destroyed chip. Don't depend on the thermal protection as a matter of course. 
D1 is unnecessary for a 7805 or 7806, only for higher voltage regulators (and only where the input voltage can be actively discharged). It provides another possible path for failure to short, so I suggest leaving it out unless there is some way the output can (say) get connected to a 12V battery and you don't have a TVS or crowbar on the output.  
The power supply does not care about load inductance- the inductance will only tend to make the current continue to flow in the same direction. Any flyback voltage appears across the switch so you need a flyback diode to be placed across the switch or the load. 
You might want to put a reverse-biased diode across the output in case two supplies are connected in series and one is driven negative. If you use a unipolar TVS that can serve both functions with a single part. 


TL;DR: Put a polyswitch fuse in series with the input (before the capacitor) and add a TVS to the output, and lose D1 (if 7805/6). For extra points mount the polyswitch close to the regulator so it sees the heat.