President Reagan campaigned across the South today, hammering at Walter F. Mondale as a threat to national security on a swing designed to bolster Reagan's confidence and boost Republican turnout in the region.

Reagan criticized Mondale by quoting Democrats who ran against Mondale during the race for the Democratic nomination. He observed that Sen. Ernest F. Hollings (D-S.C.) called Mondale "naive" on arms control issues and quoted Ohio Sen. John Glenn's criticisms of Mondale for opposing the B1 bomber, the cruise missile, the Nimitz carrier and other weapons systems.

"Now I don't know whether he would outlaw slingshots, but he would jeopardize the security of this nation, and we're not going to let him," Reagan said.

Reagan also invoked President John F. Kennedy's name to attack Mondale. "Were he Kennedy alive today, I believe he would be ashamed of those in the liberal Democratic leadership who would weaken our defense, endanger our security and sell out the cause of freedom in Latin America," Reagan said.

Mocking his Democratic challenger's claim that he is "ready to be president," Reagan said Mondale's election would mean a return to the "horrors" of high interest rates and declining productivity.

"You know, I think he's more ready to be our problem than our president," Reagan said at a City Hall rally here.

Earlier, in a speech to University of Alabama students and faculty in Tuscaloosa, Reagan ridiculed Mondale's frequent appeals for southern support.

"I think when he comes down here and says his ideas are best for the South, he's handing you the ultimate Mason-Dixon line," Reagan said. "Buying his economic policies is like going to a used car lot to buy the lemon you got rid of four years ago."

Reagan's visit to Alabama, Georgia and South Carolina today is expected to be his last southern trip of the campaign. In each of those states, his polls show him leading Mondale by 20 points or more.

Reagan's campaign strategists consider the South his strongest region and the only one in which his margin has remained steady since his Oct. 7 debate with Mondale in Louisville.

"But you can't take a political base for granted," said Lee Atwater, deputy campaign director of Reagan-Bush '84. "We face the twin demons of apathy and complacency, and there's not a better political weapon for turnout in the South than a visit by the president."

Another purpose of the southern swing, which drew large and friendly crowds, was to put Reagan in a positive frame of mind for his second debate with Mondale, which will be Sunday in Kansas City.

Last Friday, on a train trip through Ohio, Reagan unveiled a speech drafted by veteran campaign speech writer Ken Khachigian. The speech discards the incumbent's strategy of ignoring his opponent and instead challenges Mondale in a style Reagan used when he was seeking office.

Reagan's style today was deliberately low-key. He stopped at a McDonald's in Tuscaloosa to eat a hamburger and french fries. "What am I supposed to order?" he asked aides.

Reagan also answered questions from students at the University of Alabama and made a point of calling this to the attention of reporters, whom he last faced in a news conference on July 24.

In answer to a question about why he had changed his position and signed legislation that in effect imposes a drinking-age limit of 21, Reagan said he had studied the statistics of what had happened with a lower drinking-age limit and concluded, "I just thought your lives were worth it."

At one point Reagan forgot a question asked seconds before and said, "Help me out." The student repeated the question.

Sen. Strom Thurmond (R-S.C.) brought up the age issue in introducing Reagan in Greenville, S.C., at a rally at Greenville Technical College. "Ronald Reagan rides horseback and chops wood. He takes exercise. He watches his diet . . . . It's not his chronological age; it's his physical condition. He's not too old. He's nine years younger than I am," Thurmond said.