The qualifications I recommend are your basic racing pit crew safety gear. Helmet, full Nomex suit and a safety man with extinguisher handy. Man, that would be a sight at the local Gas 'n Go!
Seriously, I cannot recommend leaving the engine running. Yes, I've done it too.
First, sparks, spills, etc. could incinerate you, your car, and the station. 6 o'clock news stuff, that!
Second, I heard of cases where someone pulled up, filled up, and left the keys in the ignition. As they went to the window to pay, a low-life slid into the car, now full of fuel, started it and drove off!
With the motor running, it's even easier.
If you have a hard time re-starting it, get it fixed, don't leave it running.
'96 E300D 60k mi (wife's daily ride)
'95 Audi 90 120k mi
'92 GMC Suburban 139k mi
'85 300SD 234k mi (my daily ride)