President Reagan drew on a number of familiar anecdotes and arguments last night to bolster his plea for increased spending on arms. The record shows some of them to be in dispute or incorrect.

Reagan stated, for example, that his administration's backing of the MX missile, Trident submarine and other nuclear programs "represents the first significant improvement in America's strategic deterrent in 20 years."

However, the construction of five of the seven Trident submarines was started before Reagan was first inaugurated in 1981. Intercontinental ballistic missiles were outfitted with multiple warheads throughout the 1970s. During the Ford and Carter administrations, the Air Force developed highly accurate, air-launched nuclear cruise missiles and modernized its Minuteman III missile force with new, more accurate and more powerful Mark 12A warheads.

During the "supposed decade of neglect in the 1970s," as Sen. Carl M. Levin (D-Mich.) has said, the United States added more strategic nuclear warheads to its arsenal than the Soviets.

Reagan also said the nation he inherited was suffering from "years of declining defense spending." But Defense Department documents show that total spending, after dropping during the early 1970s in the wake of the ending of the U.S. role in the Vietnam war, rose steadily beginning in fiscal 1976.

Even adjusted for inflation, according to the Pentagon, department outlays rose from $171.8 billion in fiscal 1976 to $197.7 billion in fiscal 1981, calculated in constant 1986 dollars.

Many of Reagan's statements last night are beyond dispute. Even his most dogged critics acknowledged that the past five years have witnessed improvements in military readiness and troop quality and morale, and that Congress has erected many of the "obstacles to good management" in the Defense Department.

But other statements appear more open to question.

While citing the Soviet advantage in the numbers of combat aircraft, submarines, tanks and artillery pieces, Reagan omitted the U.S. numerical lead in Marine Corps divisions, aircraft carriers, cruise missiles, long-range strategic bombers and some other weapons.

Reagan also did not mention that, when NATO and Warsaw Pact forces are included in the equation, many of the imbalances narrow. Even in 1980, Gen. David C. Jones, then-chairman of the Joint Chiefs of Staff, said, "I would not swap our present military capability with that of the Soviet Union."

"I would take some of the things that the Soviets have for their forces in terms of numbers and give them to our forces," Jones' successor, Gen. John W. Vessey Jr., said in 1982, "but overall would I trade with Marshal Ogarkov? Not on your life."

William W. Kaufmann, a defense expert at the Massachusetts Institute of Technology who has advised Democratic and Republican defense secretaries, said that even if Reagan's defense program were adopted in full, most of the gaps the president cites would remain.

"The difference will be just as large in 1991, because we're not going to buy another 35,000 tanks," he said. "Either his program is wrong or his measures are wrong. I happen to think it's, as usual, a mix of the two."

Reagan said in his speech last night that cost growth in the Pentagon has declined from 14 percent per year in 1981 to less than 1 percent after "we began our reforms." Much of that decrease is attributable to a decline in the overall inflation rate.

House Majority Leader James C. Wright Jr. (D-Tex.), in his response to the president last night, similarly appeared to ignore the effects of inflation when he said that Reagan's budget proposal would call for spending "almost four times as much on the military by the end of this decade as the nation spent during the height of the Vietnam war."

Reagan pointed to cost decreases in F18 fighter jets and added that the price of one air-to-air missile has dropped almost by half since 1981, perhaps a reference to the Sidewinder missile, which is being purchased in far greater quantities.

But other weapons, such as the Phoenix air-to-air missile, have nearly doubled in cost, according to Defense Department documents.

The Congressional Budget Office calculated last year that Reagan increased spending on tactical missiles by 91.2 percent during his first term but purchased only 6.4 percent more missiles than President Carter, in part because of cost growth and in part because more complex types of missiles were bought.

In an apparent reference to overpricing of spare parts, Reagan said that "a horror story will sometimes turn up despite our best efforts." But Defense Department Inspector General Joseph H. Sherick found in 1984 that more than half of the spare parts purchased by the Pentagon were "unreasonably priced" (36 percent) or "potentially unreasonably priced" (17 percent).

Reagan also took credit for appointing Sherick, "the first inspector general in the history of the Defense Department," but did not point out that Congress made his position independent despite administration objections.