The NFA and its allies captured nearly half the seats in parliament and will be able to form a coalition government with some smaller reform-minded groups, or maybe not. Inexperience in running a democracy is causing lots of unexpected problems. One of the more ominous ones is accusations by some Islamic conservative parties that they were cheated in the election and righteous violence might be the right response to such mistreatment. That would be a mistake, and most Islamic conservatives know it.
The majority of Libyans are not shy letting anyone know that they do not want Islamic radicals or, as they call them, "Taliban" running the country. Al Qaeda's murderous policies in Iraq, and elsewhere, have turned most Moslems against Islamic terrorism. That sort of thing obviously kills more Moslems than kaffirs (non-Moslems) and is thus unacceptable. But local opposition does not always stop the Islamic terror groups from trying to impose their will anyway, after all, they are on a Mission From God.
Speaking of law, most Libyans indicated they want law based on Sharia (Islamic law) but now Sharia itself. Women want equal (or at least more equal) rights and everyone wants a modern (rather than medieval) version of Sharia.
The newly elected government is encountering resistance from over a hundred armed militias who refuse to hand over 5,000 prisoners. Most of those held are considered Kaddafi loyalists or "war criminals" (for killing civilians during last year's revolution.) The government has been able to prevent mass executions of these militia prisoners, but there is no judicial system to try them, or functioning prisons to hold those convicted. The government has taken control over two dozen jails throughout the country, but has not been able to put all of them back into operation. The NTC itself holds about 4,000 prisoners.
There are still towns and villages in the interior that are dominated by pro-Kaddafi militias. The government has been too busy trying to keep the peace on the coast (where most Libyans, and independent minded militias, live). But eventually, the thousands of armed Kaddafi diehards will have to be dealt with.
July 16, 2012: In the southwestern town of Ghadames (on the Algerian border) tribal raiders attacked and killed seven people and wounded over twenty. The raiders were from one of several black African tribes that fled the cities after Kaddafi was defeated. Black Libyans were seen as Kaddafi loyalists (although most were not) and generally persecuted by the rebel militias.
July 15, 2012: Attempts to crack down on corruption have caused more problems. For example, over 200 Libyans staged a violent demonstration outside the Libyan embassy in Jordan. The demonstrators want the Libyan government to provide them with lots of money for medical, travel and living expenses. The Libyan government had halted these payments because most of the expense claims were false. All this was because a program last year, to provide medical treatment abroad for wounded rebels.
The program was soon corrupted (not unusual in Libya). Local militia and tribal authorities were allowed to decide who was eligible to go abroad for treatment, and the NTC provided cash for that purpose. But soon anyone with the right connections, or a large enough bribe, got a trip to a European or Moslem country for "medical treatment." Many of those going abroad on this program were not ill, but they got to take family members as well and expected the NTC to pay them a stipend (several hundred dollars a month) while they were abroad. But many of these travelers were actually migrating, and the NTC cut off the stipends and cracked down on who was going. The NTC had to do this, because the "medical treatment abroad" program was draining huge amounts of cash from what little the NTC had, and making most Libyans (who were not in on the boondoggle) angry.
July 13, 2012: In Jordan, 150 Libyans who had just completed police training, rioted when told that the Libyan airline that was to fly them home had delayed their flight. The riots led to buildings being burned down and the use of Jordanian riot police to end the violence.