Rep. W. Henson Moore (R-La.), the front-runner in the Senate race against Democrat Rep. John B. Breaux and 12 other candidates for the seat being vacated by Russell B. Long (D-La.), aired a commercial on black radio stations in which one person asks another:

"On Nov. 13, 1979, what Democratic United States congressman from Louisiana opposed the bill to make Martin Luther King's birthday a national holiday? "

The conversation continues: "John Breaux? John Breaux opposed the Martin Luther King birthday? I didn't know that."

And finally: " . . . He's not telling it."

But there is something the ad itself is not telling listeners: Breaux, who opposed making King's birthday a national holiday in 1979, voted for the bill in 1983, when it passed.

And one more fact the ad doesn't tell listeners: Moore voted against the bill both times.

Moore's campaign press director explained, "The ad was intended to set the record straight. John Breaux does not want to tell the whole story. He flip-flopped on the issue."

Ray Strother, Breaux's media consultant, called the ad "a Republican dirty trick." Lieutenant Governors Make a Difference

Republicans are learning the value of No. 2. In two southern states -- where Democrats hold the governorship -- lieutenant-governor choices may be helping Republicans in their efforts to move into the governor's mansion.

In Florida, a poll released this week shows that long-shot contender state Rep. Tom Gallagher has moved into a tie with front-runner and former Tampa mayor Bob Martinez in the Sept. 2 Republican gubernatorial primary race, a gain made since he signed up state Rep. Betty Easley for lieutenant governor. Even state Democrats acknowledge that the two make a good match. Democratic Speaker-elect Jon Mills said, "She adds a lot of substance to the ticket, and he looks good on TV."

In South Carolina, GOP sources said their polls show Lt. Gov. Mike Daniel (D) holding a 1 percent lead over Rep. Carroll A. Campbell Jr. (R-S.C.) in the race to succeed Gov. Richard W. Riley (D). But when the Republican ticket of Campbell and Rep. Thomas F. Hartnett (R-S.C.) for lieutenant governor is matched against Daniel and his ticket-mate, state Sen. Nick Theodore (D), the Republicans have a 5 percentage point advantage. There's a glitch, however: Even though Campbell and Hartnett bill themselves as the dream ticket, the voters must pull two levers instead of one. Republican Forced Into Sept. 9 Primary

Connecticut Republican Richard Bozzuto, after running unsuccessfully for the GOP nomination for U.S. Senate in 1980 and governor in 1982, has won his party's endorsement for governor. But he failed to win the nomination outright when Gerald Labriola, the GOP nominee for lieutenant governor in 1982, and state Rep. Julie Belaga each won the 20 percent delegate vote needed to force a Sept. 9 primary.

The nominee will face Gov. William A. O'Neill (D) on Nov. 4. The last time the GOP won the governorship was 1970. Democrats outnumber Republicans by 3 to 2. Getting California In on Super Tuesday

If California Democrats have their way, March 8, 1988 -- the date of the southern regional presidential primary -- will not be the sole province of the South. The executive board of the California Democratic Party approved a measure to move the date of the state's primary from June 7 to March 8 (second and third choices are March 15 and April 12).

The measure will be introduced at the fall session of the legislature, which is controlled by the Democrats. If it passes, Gov. George Deukmejian (R) will have the choice of signing or vetoing the bill. Deukmejian said he needs to be convinced.

Democrats pushing the idea argue that California, with its 345 Democratic National Convention delegates, has been left out of the election process. "We are 10 percent of the population," said one Democrat, "we want to have some say." Marathon Man Pedals Ambitions in Iowa

Having just completed a 497-mile, week-long bike ride across Iowa -- including 16 interviews with local television stations -- Arizona Gov. Bruce E. Babbitt (D) will test his legs, and his 1988 presidential ambitions, in New Hampshire next. In August, Babbitt plans a 23-mile hike to the summit of Mount Washington, the highest peak in New England, with a group of state Democrats and environmentalists.