The Tuesday Team Inc., Reagan's advertising group, had a little slip-up this month. In one 30-second television commercial that aired nationwide during prime time, one crucial fact was omitted: A man who suggested on camera that he found work because of Ronald Reagan actually got his job while Jimmy Carter was president.

Larry Headley, an accountant from Woodbury, N.J., was originally filmed by a Reagan campaign camera crew in July 1980 as he walked out of an employment office. "I've been out of work since April," he said then, "and I'm still looking for a job." He eventually appeared in a Reagan spot that aired during that year's campaign.

Thinking they might have a nice "Are You Better Off Now?" commercial in the making, Reagan's advertisers contacted Headley this fall. Sure enough, he had a job. A camera crew was dispatched to his house. "Things have sure changed," Headley said as he looked into the lens, having memorized a text that the advertising team "had helped me to construct." He then added, "Today I have a job and I have a future. It's Mr. Ronald Reagan's policies that have made the difference in our lives."

The spot, combining the before and after sequences, aired nationally the week of Oct. 1. But Headley, after five months of unemployment, found his job in the fall of 1980. "It was probably before the election," he said in a telephone interview from his home.

Still, Headley says he's going to vote for the president. "Mr. Reagan did not introduce me to my employer, and we didn't imply that in the ad," he said. "The point is, the business I'm in has flourished in the last four years."

Reagan campaign officials say they didn't find out until after the spot aired about the timing of Headley's employment. Because of that, they say, they pulled the spot a day early. Asked why Headley neglected to tell them of the timing, Reagan-Bush media director Doug Watts replied: "Beats me."