Printing issues meant voting papers for the landmark poll did not arrive from South Africa until Friday evening.
An overnight attack on election HQ in Abuja failed when a petrol tanker laden with detonators failed to explode.
The election should result in the first transfer of power between civilian presidents since independence - but BBC reporters across the country are reporting numerous problems.
l Voting began on time in some parts of Katsina, home of two of the main presidential candidates, but near an election office youths burnt down several shacks, expressing frustration and anger at problems in getting election materials there.
l There were delays at many polling stations in the capital, Abuja, with the late arrival of election materials or officials, despite lines of people waiting to vote.
l A low turnout was reported in Lagos in the south, with some local voting cancelled after details on ballot papers were missing.
l Violence and long voting delays were reported in the Niger Delta.
l Few polling stations have opened in north-eastern states by Saturday
l The electoral commissioner in Enugu in eastern Nigeria had to wait at the airport for election materials to arrive.
l High turnout was reported in Panshekara, on the outskirts of Kano in the north, the scene of a clash between Islamists and security forces earlier this week
The run-up to the poll has been marred by violence - more of which broke out on Friday night.
Police say a petrol tanker laden with gas cylinders was used in the failed attack on the electoral commission's headquarters, from which the elections are being co-ordinated.
The attackers attempted to roll the unmanned tanker into the building, but the tanker missed its target, crashed into a lamp post and came to a halt.
Though there was a small fire on board the detonators failed to trigger a large explosion.
More violence is also being reported in Bayelsa in the oil-rich south, the scene on Friday evening of a possible assassination attempt by militants on the state governor and ruling party's vice-presidential candidate Goodluck Jonathan.
The BBC's Abdullahi Kaura says people he has spoken to in Yenagoa, the capital of Bayelsa, say the streets are deserted and heavy machine gunfire and explosions have been heard.
There have been fears for the credibility of the parliamentary and presidential polls after allegations of widespread fraud in last weekend's state elections.
Outgoing President Olusegun Obasanjo said despite flaws, Nigeria could achieve a peaceful and democratic handover of power.
He urged aggrieved candidates and their supporters to "explore all avenues for seeking redress" rather than resorting to "jungle justice" in the aftermath of the vote.
The Independent National Electoral Commission (Inec) delayed polling by two hours after they reprinted the ballot papers to include the Vice-President Atiku Abubakar following a court ruling on Monday.
Abubakar is considered one of the leading contenders for the presidency, alongside Umaru Yar'Adua of the ruling People's Democratic Party and former military ruler Muhammadu Buhari.
However, it is not clear how Inec planned to distribute the materials across the vast country with a very poor road network and unreliable airport facilities, says the BBC's Senan Murray.
EU observers say they are concerned about the credibility of the vote after last weekend's flawed state elections.
Unrest before and after those polls left up to 50 people dead.
UK MEP Edward McMillan-Scott in Lagos denounced the vote as "shambolic" and "second rate".
Nigeria is Africa's most populous country and is one of the world's biggest oil producers. It is of key strategic interest to both the West and the growing economies of the East.
But despite the country's huge oil wealth, tens of millions live in poverty.
60m registered voters
120,000 ballot boxes
360 House of Representative seats to be elected
109 Senate seats to be elected
24 presidential candidates
Main contenders:
l Atiku Abubakar for the AC, 60-years-old
l Muhammadu Buhari, ANPP, 64
l Umaru Musa Yar'Adua, PDP, 55
