I thought it was against the law to have the gas turned on when you are towing. It is certainly a bad idea, if something were to fall and knock a gas ring on for example.
I did forget once to turn it off. I was surprised to find the fridge hadn't even blown out.
I wouldn't dream of travelling with the gas ON, that would just be suicidal (and probably class as murderous too....) I wondered whether people disconnected as opposed to just turning off. It's fairly academic anyway as presently we have Propane with a Quick-on reg, I just wondered for when we change to nice, sensible Butane!
I always disconnect regulator and refit the plastic cap, but ours is only a click on one not the screw in type, the bloke at Oakleys Gas was a bit off with me because I took the bottle into the shop without the cap replaced!(think he mustve been a HSE freak) I think the screw in type would probably be ok left connected as they are more secure than the type we have which could get knocked off in an accident.