Lindsay Roy won the seat with a majority of more than 6,000
The counting of the votes after the Glenrothes by-election was not as "transparent" as it could have been, according to the elections watchdog.
The Electoral Commission said the conduct of the count, last November, "went smoothly despite many challenges faced by the electoral administrators".
However, it said some areas where the votes were being counted and collated were obscured from view.
It also voiced concern over aspects of the arrangements for postal voting.
Lindsay Roy held on to the Westminster seat for Labour with a majority of more than 6,000 in the by-election, which was held following the death of sitting MP John MacDougall.
In a report on the administration of the by-election, the Electoral Commission said it was run well by Fife Council in difficult circumstances.
But the commission report stated: "We do have some concerns that the count was not as transparent as it could have been, due to the layout of tables in the hall.
"One table where votes were being counted was not clearly within the view of candidates, agents or other observers.
"Also, the central tables where the votes for each candidate were collated were situated behind the returning officer's platform and obscured from view."
The report also said the first opening of returned postal votes did not take place until the day before polling day.
Had this been done sooner, the commission said, a problem which arose with the electronic scanning equipment used to help adjudicate postal votes could have been resolved more quickly.
"The timing of the postal vote openings and the potential consequences of that timetable gave us cause for concern," stated the report.
Despite the criticism, Andy O'Neill, head of the Electoral Commission in Scotland, said: "All stages of the election - from registration of electors to the counting of votes - went smoothly despite many challenges faced by the electoral administrators responsible for running the poll.
"Fife Council also ran an extensive campaign to get people registered to vote, even though there were only seven working days between the writ being moved and the deadline for registering."
The Electoral Commission also welcomed an independent investigation after the courts lost marked electoral registers for the by-election.
The registers, which are the only record of who voted, must be kept for a year.