Many people have written that this is a social problem not a technical one. Here's why they are wrong.
I have been to Egypt on many trips and have seen firsthand the problems described above. In egypt, there is rampant corruption in the government. That trickles down to all agencies. The people who pay taxes do not get anything in return. Nobody obeys traffic laws there. People frequently cram 6 cars into the equivalent of 3 lanes of traffic. People believe the lines are for decoration. In the areas where there are traffic lights, nobody obeys them. The only person people obey is soldier with the machine gun directing traffic. They are groomed with the understanding that as long as they don't piss him off they get away with everything else.
What people are asking him is to essentially revolutionize the government and make it work. The people only understand money. If you have money, you get what you want. If you don't, you end up with the above situation.
As an example, a number of years ago I witness a car accident on a busy street which backed up traffic for miles. It was between a guy on a motorcycle and a guy in a car. The two drivers started fighting in the middle of the street and a crowd of people developed. The soldier didn't care about the people involved or the damage to the vehicles. He pointed his gun at the crowd and told them to move the cars or else. The crowd moved the vehicles on the sidewalk and they to got on the sidewalk. The fight continued but traffic started moving again.
For your technical solution, there are going to be lots of caveats. In Egypt, for example people will steal just about anything. I have seen people steal electricity, phone lines, natural gas, side-view mirrors on cars just about anything. If you create this system, theft will be a big issue. If you can guarantee that know one will steal your system that is your first hurdle. Soldiers in egypt are paid so little that they may not care for your system - especially if the guy who broke the law will pay them a bribe directly on the spot versus paying a fine to a higher up agency where he will never see his cut.
If you can start with the block that you live on and mount webcams (*note -- In egypt, this will run you afoul of the government and the soldiers regardless of your intent!) on your building to prevent theft then you can log all the cars coming and going. This would make it easier to identify who the parties in the accidents are in case someone flees.
Speedingwise, I have seen stories of how people take apart optical mice and use them as sensors. There is probably a cheap way to rig this to give you timings of start/stop points. You could then time how long it takes a vehicle to cross two of these sensors to determine rate of travel. If you take snapshots of the clock time at both locations, you could do a look up against the snapshots from your webcam. Or you could use this to determine when to take snapshots on the webcam.
This is basically how the toll road cameras work here in the states. Even if the driver gets away, you can at least identify the driver in the future.