Thursday's vote pitted Yoweri Museveni, the incumbent president, against his former doctor who has become the biggest challenger to his 20-year grip on power.
The latest opinion poll gave 62-year-old Museveni 47% and 36% to Kizza Besigye, 49, of the opposition Forum for Democratic Change (FDC).
As a predictable row erupted even before all polling booths had closed, the country's ruling National Resistance Movement (NRM) dismissed the complaints as coming from "bad losers".
From the shores of Lake Victoria to a remote war zone in the north, long queues of Ugandans braved alternate sun and downpours to vote in the election.
While there were widespread complaints of names missing off voter registers, and some other scattered reports of irregularities, there was no serious violence as many had feared after a volatile election campaign.
Sam Akaki, FDC spokesman, said "multiple irregularities" were detected during Thursday's vote and the party was mulling a legal challenge.
"I think the opposition are bad losers. ... Voting is supposed to be secret. Why do they think all the missing names are their supporters?"
Ofwono Opondo, the NRM spokesman
He cited "illegal" and intimidating deployment of soldiers close to voting booths, the use of ink "that can be washed within two seconds", multiple voting by government supporters, and names missing off electoral registers.
"It has gone very, very badly," he said. "The government does not want free and fair elections."
But the ruling NRM dismissed the complaints saying the election was free and fair.
"I think the opposition are bad losers ... Voting is supposed to be secret. Why do they think all the missing names are their supporters?" Ofwono Opondo, the NRM spokesman, said.
"We need to differentiate between technical hitches and political motives," he said, adding even his younger brother had been unable to vote for the Movement as he was not listed.
There are almost 20,000 polling stations across the nation and official election results are due by Saturday; but some counting stations began declaring immediately.