Several ballot papers in at least four constituencies were deemed inadmissible as they had not been stamped at polling stations.
An investigation has been ordered into the rejection of 72 ballot papers in Waterford because they were not stamped.
Presiding officer Niall Rooney has told candidates he plans to investigate the failure of staff to stamp ballot papers as required before they are handed to voters.
Mr Rooney said it was not clear at this stage whether the problem with unstamped ballot papers arose in a small number of locations or was more generalised across the county. However, he promised whoever was responsible would not work on future elections.
The 80 unstamped ballots were among 400 spoiled votes in the constituency.
Independent candidate in Wexford John Dwyer has claimed that as many as 380 voters from the New Ross area were disenfranchised after ballot papers were found to not bear the official stamp of the count centre.
A total of 691 votes were deemed spoiled when the results of the first count were announced on Saturday evening.
However count staff said the number of ballot papers found to have been unstamped was is the order of 50, which they said were spread throughout the county.
"I am unemployed so I won't be taking a Supreme Court case or a case to the European Court of Human Rights but Robert Mugabe would be proud of this antiquated system," Mr Dwyer said.
Mr Dwyer said he believed a large number of spoiled votes in Wexford were the result of the stamping issue, while others were “pro-lifers who decided to protest in that way, the clowns. Imagine people died so those clowns could vote,” he said.
Mr Dwyer was eliminated after the fifth count having garnered 1,362 votes.
Independent TD Tommy Broughan expressed concern about 700 spoiled votes of which 150 were not stamped at polling stations and were deemed invalid for the Dublin Bay North contest. It was the last constituency in the State to declare a first count. Mr Broughan said seats could be decided on very few votes.
His director of elections Seán Clarke said “people voted correctly” and it was an administrative problem. “We don’t know what polling stations they were at” but he said “there’s a huge question mark as to what the staff were doing. And those votes are now out of the mix.”
Mr Broughan said this had happened before in the local election. “Somebody keeps making this mistake.”
In Dublin Central, candidates and their agents gathered for an adjudication of the spoiled votes. A large number had no stamp on them and were inadmissible.
An equally large number of voters had merely placed a tick beside each of their preferences, spoiling their vote.
The returning officer laid each of the ballot papers out on the table for agents and candidates, asking them not to touch them.
One paper had scrawled across it the message “F**k the election”.
Another held the message “None of these”, while a third showed a large squiggle around the ballot paper.
One voter wrote a zero beside each candidate’s name.
An intriguing element of the count was a number of voters started their preferences at number two and proceeded all the way down the paper, but failed to give a number one to any candidate.
Fianna Fáil candidate Mary Fitzpatrick questioned the decision to make a vote invalid. The voter in question had put number two and three in the box beside her name, but the paper was also initialled with "MM 1".
Under the rules the ballot is secret but the initials could identify the voter.
Ms Fitzpatrick suggested it meant “Micheál Martin number 1” and that would make it valid for her as the Fianna Fáil candidate.
The returning officer did not agree.
One voter in Dublin West did not seem to like any of the candidates on the ballot paper and added their preferred nominee for the Dáil - Conor McGregor, with a tick beside his name. No other preferences were expressed.
The ballot paper was inadmissible.