Running furnace while driving - Ok?
Somewhere along the road to Caution you cross the Paranoia county line.
Several posters have voiced strong opinions about securing the propane while driving. OK, there's nothing wrong with thinking about safety. However, if you don't trust your propane system while driving, what makes you think that it's any better when parked? If it does indeed leak, you're probably LESS safe using it while parked, because there is less outside air movement to dilute and move the propane away from your rig.
So, if you secure the propane, let's think about the electrical system for a minute. Anyone ever hear of wire insulation wearing through and causing a short? This is also a fire hazard. So, shouldn't we also disconnect all our batteries and not use the generator (or shore power, if we don't trust the insulation)?
Then, gasoline can go "boom", too. A fuel leak onto the exhaust manifold can cause a fire...
This might lead you to want to live in a cave. Oh, scratch that, too. Special Forces might mistake you for Osama Bin Ladin and attack!
Therefore, if you are uncertain about the status of your propane system, I would suggest only putting a few gallons in it for a day, and see if you smell anything, the level goes down unexpectedly, or the propane detector goes off. If it passes this, I frankly wouldn't worry too much about it. You've got a lot more pressing things to worry about while driving an RV all that distance than whether your propane is going to blow up or not. As you might have guessed, I leave mine on (except for going through the odd tunnel or ferry which requires you to secure it).