When visiting Jerusalem, you will surely be approached by numerous taxi drivers offering to drive you to Bethlehem. One driver pulled over on a busy street to solicit us. After we said no, he backed up and kept making offers to us for about 50 meters.
If you do hire a driver to take you to Bethlehem, make sure that he is not going to smuggle anything into or out of the Palestinian territory. Drivers figure that they will have less scrutiny at the security check-point if they are transporting tourists. They can also pass the blame onto you, saying that the contraband is yours.
If you are driving to Jerusalem area from the center of Israel (Route no.1) don't drive too fast - the road can be tricky.
Also - if it is winter it can be foggy and slippery.
While returning from En Kerem i saw 2 car accidents.
Traffic in the vicinity of the Jerusalem Shopping Mall is disrupted frequently(2013) by road works and traffic jams caused by the nearby football stadium.
Also extensive road works on the main highway to Tel Aviv cause slow-downs.
It is VERY difficult to find parking in Jerusalem. There are meters( about 4 shekels per hour) but if you overstay your limit or park illegally there are steep fines. Better use public transport or walk.
Make sure that the car you will get into is an acredited taxi or sherut service, otherwise you will find out on your way to the airport that they are NOT allowed to enter the airport departures area.
We gort on this cab that didn't actually have a cab sign and we ended up at the airport entrance, where we had to say what the cab driver asked us to, that we know each other for a long time and he came to get us to the airport. He was a muslim guy and his name was Ismail.
The police at the airport entrance stopped the car, got all our stuff out, checked the car with police dogs and put us in separate rooms to ask us if we know each other, for how long and so on.
In the end, they let us go, but after all the emotions.....
So, be aware something like this won't happen to you too.