Balloting on the second and final day of specific early voting did not begin on time in at least one province after the Zimbabwe Electoral Commission failed to deliver materials, including ballot boxes and voters roll to sign, Africa Review reported.
Witnesses said voting in polling stations elsewhere began in the evening.
Africa Review said it received reports of many people being turned away because their names weren't on voter rolls.
"Voting at most polling stations started at a slow pace at most centers," Joyce Kazembe, ZEC deputy chairwoman Joyce Kazembe, said Sunday.
"This was mainly due to the fact that we delayed dispatching ballot papers to the centers," Kazembe said. "I wish to advise that the printing of ballot papers delayed even beyond our expectation."
Kazembe said the commission was confident all eligible voters could vote despite the chaos.
"We admit we underestimated the process," she said. "By next week all ballot papers for July 31 will be ready."
Balloting is limited to 260 polling stations.
Prime Minister Morgan Tsvangirai told supporters in Masvingo Sunday the confusion indicated Zimbabwe was not ready for a free and fair election, Africa Review said.
"We gave ZEC the powers to oversee a free and fair poll," he said. "The question is if ZEC has failed to run the special voting ... how then can it administer a national poll."
The government estimates about 70,000 police are eligible to vote, but Tsvangirai has disputed that number, expressing concern that security forces would try to manipulate the election in favor of President Robert Mugabe and his Zanu-PF party.