Voting in the District of Columbia went smoothly yesterday with dramatically fewer mistakes than in the Sept. 14 primary. Election officials said the improvement came because they had significantly updated the voter rolls.

At 11 p.m. yesterday, D.C. elections officials reported that only 542 voters had to cast special challenged ballots because their names could not be found on official voter lists and they did not have sufficient identification. Officials at the D.C. Board of Elections and Ethics said they believed that is the final total of special ballots.

In figures released at 8 p.m. yesterday, officials estimated another 500 to 1,000 others who had gone to the polls by 1:30 p.m. without any proof of registration had voted regular ballots by signing affidavits.

Another estimated 1,000 to 1,500 voters who found their names missing from voter rolls before 1:30 p.m. yesterday were able to cast regular unchallenged ballots simply by presenting their voter registration cards. There were 55,491 ballots cast at that point, according to the elections board.

Officials said late last night they would not have a final count until today on the number of people who used voter registration cards or affidavits in order to vote.

By contrast, some 20,000 legitimately registered voters in the primary had found their names mistakenly dropped from the voter rolls and were forced to vote special challenged ballots.

In order to avoid a repetition of that, the elections board passed emergency rules allowing registered voters whose names did not appear on the official list to cast regular ballots by signing an affidavit or presenting registration cards. But at the same time they rushed to add the names of the 20,000 to the voter rolls.

"This election is a 100 percent improvement over September and a 1,000 percent improvement over last November," said elections board Chairman Albert J. Beveridge III yesterday as he toured 10 precincts. In the November 1981 election there also were problems with many voters being mistakenly dropped from the rolls.

Beveridge said the turnout was good. Workers in these precincts and many others visited by reporters yesterday said they were pleased and things were going smoothly.

"Maybe everybody expected problems psychologically, so everybody brought in identification . They came prepared," said Elenore Creamer, precinct captain at St. Thomas Church in Ward 2.

"Voting procedures are going a lot better," said Mayor Marion Barry as he toured polling places in Northwest. He praised David Splitt, acting executive director of the D.C. Board of Elections and Ethics, for "doing a good job notwithstanding all the criticism of the system . . . He took a bad situation and made it better."

Splitt was delighted yesterday. "We've gotten the vast majority of people dropped from the list in the primary on the list," he said. "There was no way to insure in that short a time that we would get them all on correctly . . . In 30 days it was very hard to achieve perfection out of chaos."

Beveridge said yesterday Splitt will leave his position in the elections office after yesterday's results are certified, as planned. But the mayor said yesterday he will talk to Splitt about staying on.

Election officials said they were able to add to the rolls or correct in recent days the names of about 500 people who checked their names at voter lists posted in city libraries, and finding them missing or incorrect, mailed in corrections.

At Precinct 51 yesterday--the Lafayette School at Broad Branch Road and Northampton Street NW--974 people had voted by 2 p.m., which officials said was a good turnout. Of that number only six people filed affidavits to vote and two filled out special challenged ballots. Some 29 people had showed voter registration cards to vote when their names could not be found on the rolls.

"There were virtually no problems compared to last time," said Nancy Wright, the precinct captain.

Under the first of two emergency rules passed after the Sept. 14 primary, a voter whose name was not on the rolls was able to cast a regular unchallenged ballot yesterday after showing a registration card.

Under the second, more controversial, emergency rule a voter could cast a regular unchallenged ballot even without a registration card or other proof of registration. A citizen could do this by showing current identification like a driver's license and signing an affidavit swearing to being a properly registered voter.

This rule came under legal attack last week on grounds that it was loose enough to open the elections system to possible voter fraud, but the D.C. Court of Appeals approved the rule on Saturday after Splitt argued in an affidavit to the court that it was necessary to make the election run smoothly.

As elsewhere in the city, drivers licenses were the most common form of identification for voters who signed affidavits at the polling place at Backus Junior High School, South Dakota Avenue and Hamilton Street NE. Precinct captain Alfred H. Neal said voting went smoothly and quickly. At Backus, one of the largest polling places in the city, 473 votes had been cast by 9 a.m. yesterday. Some 41 of these were by affidavit, none by special ballot.