Chicago — Political misjudgments and mistakes are beginning to nip at Gary Hart's heels as he runs for the White House. The red-hot Hart campaign has set a blistering pace since mid-February. In recent days, however, Mr. Hart's victories have been fewer and his campaign's performance more ragged. He won very little in the state caucuses on ''Super Saturday,'' March 17. He watched Walter Mondale sweep the Puerto Rico primary on Sunday.
At the same time, news stories and television reports on the Hart campaign have become steadily tougher. And there have been signs that Mr. Mondale's attacks on Hart are having some effect.
Hart has fought back. But for the first time, the young senator has found himself on the defensive. In recent days, he has committed a series of gaffes that could be damaging.
Such mistakes may seem unimportant if Hart wins a smashing victory today in Illinois. But Hart's vulnerabilities are being carefully watched by Republicans, and could be paraded back before the voters in the fall.
Reporters following the Hart campaign saw the first signs of trouble shortly after Hart's stunning victory in New Hampshire. News stories began probing into Hart's background. Hart's opponents - especially Mondale and John Glenn - took aim at Hart's record.
The impact was swift. As often is the case in politics, Hart was probably hurt less by what was discovered, than by the way he handled each revelation.
One of the most telling TV broadcasts came right after the presidential debate a week ago in Atlanta. In that debate, two specific points were raised about Hart's record. One point related to Cuba, the other to the proposed equal rights amendment (ERA).
In the debate, Mondale charged that Hart had once said he didn't know whether Cuba was a totalitarian state. Hart denied Mondale's assertion. After the debate , Hart told reporters:
''In the incident involved, I refused to say whether it was either totalitarian or authoritarian, and it wasn't because I didn't know.''
But Bruce Morton, a correspondent for CBS News, checked the record and found the following exchange in 1982 between Hart and the editors of the Washington Post:
Hart: ''Cuba is not totalitarian and it's not democratic.''
Post: ''If Cuba is not a totalitarian government, what is it?''
Hart: ''I don't know.''
Senator Glenn had charged in the debate that Hart would use the power of the federal government to withhold projects from those who were undecided about support for the ERA.
Hart interjected: ''No, I didn't.''
But CBS noted that the record of Hart talking before the National Women's Political Caucus shows Hart saying:
''I'm talking about specific federal projects to be used to bring around people who are on the fence . . . where support is at least lukewarm, and I intend to do that.''
Hart might have been hurt in the conservative South by such stands on Cuba and the ERA; but his failure to acknowledge his positions on the issues made things even worse.
That shaky performance has been followed by others.
The subject of Hart's age, for example, seems so trite that some people consider it too silly to discuss. But Hart has kept the issue bubbling.
When first asked why his campaign literature and other sources list his birthday as Nov. 28, 1937 (when it was really 1936), Hart told a nationwide TV audience:
''I can't account for every piece of paper that's been written by my campaign or anyone else.''
Hart's birthdate, however, is incorrectly shown in Who's Who in America, Current Biography, the Congressional Staff Directory, the Almanac of Politics, and other sources, including his own book, ''A New Democracy.''
The Rocky Mountain News, in a copyrighted story earlier this month, found that Hart's voter-registration form and his driver's license both show his wrong age.
Hart had consistently listed his birthdate correctly as 1936 until moving to Colorado after attending college. The reason for the one-year change after moving to Colorado, the News said, remains ''unknown.''
In the past few days, other problems have emerged. Hart, in an emotional statement to the press last week, charged that Mondale was broadcasting a personal attack based on Hart's change of his signature, his age, and his name. Said Hart:
''I've spoken about new ideas for the future. For some reason, former Vice-President Mondale wants to talk about my handwriting. I've proposed new ways to make this economy grow again and create real social justice in the United States in the 1980s. For some reason, former Vice-President Mondale proposes to talk about what my birthday is.''
The only trouble was, Mondale had broadcast no such advertisement. He hadn't mentioned the subject of name, age, or signature.
Within hours, Hart's staff realized an error had been made. They quickly persuaded him to apologize. His unprovoked broadside at Mondale was blamed on a staff mistake.
As the Illinois primary neared, Hart appeared to swing back and forth on an ad of his own that attacked Cook County Democratic chairman Edward R. Vrdolyak, who is backing Mondale.
The ad portrayed today's vote in the Prairie State as a contest between Mondale (representing ''the bosses'') and Hart (representing ''people who think for themselves.'')
After the ad was broadcast on Friday, Hart said it had been put on the air by mistake - prompting Mondale to say that his opponent was showing ''unsureness'' and ''uncertainty'' in his campaign. Then on Sunday, adding further confusion, ABC-TV said it had learned that the Hart ad was still being shown on at least one Illinois station.
Even as all this was unfolding, Hart had another problem. The Wall Street Journal reported that when he was in high school, Hart, according to one of his former teachers, had swiped a copy of his forthcoming chemistry exam. The teacher, Lester Hoffman of Ottawa, Kan., told the Journal:
''I had him his senior year. He was indiscreet. He and a friend entered my classroom one night and took a copy of an examination. They were C students, and they got almost perfect answers to the 50 questions in that quiz. I was suspicious, and I found out what happened.''
Mr. Hoffman gave both boys a grade of C. ''They never came to me to talk about it,'' he said.
The Journal reported that when Hart was asked about the incident, he declined to comment.