It's certainly getting better; though I have to admit that I've never found it that bad, at least not compared with Cairo or Lebanon.85% of Jordanian drivers are good or very good; 10% are not; leaving 5% who should never be allowed near anything that might try to move along any paved surface! seriously! I have seen people in the outside lane, at well over 100 kph, suddenly decide to turn right, and only look around afterwards.
But that's why the other 85% are good; they are constantly vigilant, they expect anything to happen and regular personal experience has equipped them to cope.
Please don't be put off. If you're a reasonably competent driver anywhere else in the world you'll be fine in Jordan. If you are a bit anxious then stay out of the capital Amman and you will have no problems. We can arrange for your hire-car to be waiting for you at the airport and the drive to the Dead Sea or to Aqaba from there is very straightforward.
Do not speed though! At least not on long straight stretches of road if you can see anything that might be a vehicle in the distance. In the last few years the police have learned all the tricks for catching fast drivers.
It is a fair game. They wait, if you're well over the speed limit they step out and wave at you and give you a fine on the spot. I have never heard of anyone being fined for speeding when they were not speeding and I have some personal experience of being able to blag my way out of awkward situations!
Sometimes, much to the discomfort of most Western drivers, you get stopped for no reason; perhaps because the guy wants to practise his Englis! I'm a bit resistent here, if I have clearly been doing nothing wrong at all. And often they will then just wave you on. Explanations that it's all for my own safety and security don't stand up to examination. They may want to stop locals to know who's going where, but in general they're not supposed to stop and hinder tourists; and to be honest in general they don't.
Be careful when you're filling up your car. Self-service is more or less non-existent. But, after a couple of bad experiences, I always get out of the car before unlocking the petrol cap! You need to check the petrol pump is at zero before they start fuelling you up, or you'll be paying for the previous customer as well as yourself! It's not that common but pretty annoying when it happens.
Finally, beware of sleeping policemen! They are much better 'organised' than they used to be; these days nearly all of them are marked and signed in advance and only a few are so unsubtle as to risk permanent damage to your suspension if you're travelling faster than 18kph.
If you drive with normal awareness, good sense and courtesy, then you'll have a great time on the roads of Jordan.