The national leadership of the Democratic Party descended on this state yesterday in an attempt to patch over the differences in the faction-ridden Minnesota Democrat-Farmer-Labor Party before the Nov. 7 election.

President Carter and Vice President Mondale, making a rare public appearance together outside Washington, attended an airport rally here yesterday afternoon, appearing side by side with the DFL's three statewide candidates, Sen. Wendell R. Anderson, senatorial candidate Robert Short and Gov. Rudy Perpich.

The theme was party unity, a dwindling commodity here since the conservative Short upset DFL-endorsed Rep. Donald M. Fraser in the Democratic primary last month.

Invoking the name of the late senator Hubert H. Humphrey (D-Minn.), whose death earlier this year was followed by considerable bickering in the state party he was instrumental in founding, Carter appealed to Minnesota Democrats to remember the lessons of Humphrey's 1968 presidential campaign.

"Hubert Humphrey lost in 1968 because the Democratic Party was divided," the president told about 3,000 people jammed into an airport hangar here.

"Because the Democratic Party could not heal its wounds after the 1968 convention in Chicago, Hubert Humphrey was not elected president and Richard Nixon was . . . I urge you to remember Hubert Humphrey, to remember what happened to him when our party was divided."

The state party divisions were symbolized by Short, who appeared at the airport rally and later flew with Carter and the other candidates on Air Force One to Minneapolis for another rally last night. But at neither event, which White House officials said were arranged by the DFL, was Short scheduled to speak. Anderson and Perpich spoke at both.

Despite the divisions and the fact that Short and the liberal Anderson and their supporters at times are clearly at odds with one another there have been recent indications that the president's appearance in Mondale's home state coincided with a rise in Democratic fortunes.

Anderson and Short are now given close to an even chance to win their races, while Perpich has a growing lead in his race against Republican Rep. Albert H. Quie, whose old district includes Rochester, where Democrats also hope to score a win.

The president flew to Rochester and on to Minneapolis after stopping in Wichita, Kan., where he plugged the candidacies of former Democratic representative Bill Roy, who is running for the Senate, State House Speaker John Carlin, who is seeking the governor's office, and Democratic House candidates.

The trip marks the beginning of Carter's final campaign push in the congressional elections. Between yesterday and election day, he is scheduled to make five campaign trips into 12 states for Democratic candidates.

The president also used yesterday's trip to sign two bills of particular interest to the states he visited.

In Kansas, he signed the Agricultural Trade Act of 1978, designed to increase U.S. agricultural sales abroad, and he strongly defended the administration's farm policies.

But outside the Century II convention center in Witchita, about 1,000 farmers, member of the militant American Agricultural Movement, protested those policies. They distributed bumper stickers bearing the slogan, "Jimmy Carter is a parity pooper."

In Minneapolis last night, the president signed the waterways users legislation, which for the first time will impose fees for the use of federally maintained inland waterways such as the Mississippi, with the revenues to be used to upgrade the waterways.

At a Wichita rally, for Roy, Carlin and other Kansas Democrats, Carter stuck to his standard, basically conservative campaign speech. The impact any president can have on mid-term congressional elections is problematical, but the visit to the heart of the Farm Belt provided fresh evidence that Carter's political fortunes are on the upswing.

A simple mention of the Middle East summit conference - "We had good luck at Camp David," Carter said - brought a sustained ovation from a crowd of about 4,000 in the convention center.

En route to Kansas with Carter, Democratic National Committee Chairman John White said Roy is now given a good chance to win his Senate race against Nancy Landon Kassebaum, the daughter of 1936 Republican presidential candidate Alf Landon. White said Carlin, facing a tough race against Republican Gov. Robert F. Bennett, should do better than expected, but he stopped short of predicting a Carlin victory.