Secretary of State George P. Shultz worked hard last week to see that the Contadora process for Central American peace, now moving into its final phase, will bear some Reagan administration fingerprints.

The treaty initiative, launched 18 months ago by Panama, Colombia, Venezuela and Mexico without U.S. involvement or the help of any international organization, has made far more progress than anyone expected. In fact, it seemed 10 days ago that a regional peace pact might be signed without more than a passing nod to Washington.

However, as Shultz said in a different context, "As soon as the possibilities start emerging, it's sort of the Jimmy Durante story: Everybody wants to get in on the act."

Shultz spent much of his recent three-day swing through Central America trying to make sure that any final Contadora pact would contain elements the State Department wants. Among these are stiffer procedures for verifying treaty terms, a detailed timetable for foreign troops and advisers' withdrawal, and tightened requirements for democratic elections.

Washington would regard any treaty without these provisions, Shultz said, as "just a piece of paper." What he did not say was that if his recommendations were added and the final product went into effect, President Reagan could claim some credit.

In early September, the Contadora talks seemed moribund. The Sandinistas, U.S. diplomats were saying confidently, would never sign any Contadora treaty.

But Sept. 21, Nicaragua announced it would sign the 55-page Contadora draft that was completed Sept. 7. The Reagan administration was caught off balance by a treaty it didn't like but had never publicly criticized.

Shultz and his party managed to talk during this trip and the preceding week to the heads of state or foreign ministers of the four Contadora nations as well as those of all five potential treaty signatories: El Salvador, Costa Rica, Guatemala, Honduras and Nicaragua. It was an effort to bring them into line with U.S. views on a regional peace pact.

"We see a significant amount of progress," Shultz said as he returned to Washington. "The issues involved are pretty clearly identified, and there are known ways of dealing with them . . . . If it's wanted, if there's a will, there's a way, and I think there's quite a lot of will."

Shultz's touchiest discussions, aside from those with Nicaragua, were with Mexican President Miguel de la Madrid and Foreign Minister Bernardo Sepulveda. Mexican diplomats had let it be known that they were irritated with Washington's sudden discovery of flaws in a treaty process it had endorsed. But Shultz apparently made his point.

"In light of observations we have received from the Central American governments," Sepulveda said Saturday at a news conference after the talks, "it would perhaps be useful . . . to perfect" certain "procedural" parts of the treaty draft. He said the changes would not affect "essential, fundamental and substantive" parts of the document.

Leaders of Guatemala, Costa Rica, Honduras and other nations also agreed that "certain changes" were needed in the draft treaty, Shultz said.

Nicaraguan officials had said they wanted the existing draft signed without alterations, and junta leader Daniel Ortega said during his visit to the United States that only "details" were omitted, especially in the treaty section on verifying the post-treaty military situation.

"These questions are asked to slow the process" so the United States will be in a better position to intervene militarily against Nicaragua, Ortega said. "The important thing is to sign the act; in the implementation these details will be taken care of."

Asked about these "details," Shultz said that some people called them technical adjustments while others called them fundamental.

"I think these labels . . . don't really lead you anywhere . . . . There's a real difference between agreeing on the idea that verification is necessary and important, and agreeing in advance that it will be done, and here's how," he said.

The draft pact now sets up a five-member Commission on Verification with powers to investigate complaints of treaty violations. State Department officials say the treaty should spell out how many people will do what kind of on-site inspections of alleged treaty violations, how much and by whom they will be paid, what notice they will have to give to the governments involved, and what kind and how many vehicles they may use with what freedom of movement within a country.

U.S. officials said that the pact also should say who gets to see the investigators' report and how violators will be punished.

All foreign advisers and military personnel shall be withdrawn from the region, the pact says, but U.S. officials say current definitions would allow Nicaragua to keep civilian Cuban and Soviet personnel while banning U.S. helpers in El Salvador and Honduras. The State Department wants a detailed timetable for everyone's withdrawal that would not force it to halt aid to El Salvador before Nicaragua ends its support to Salvadoran guerrillas, as it says the current draft would do.

Further, it wants the definition of free, democratic elections tightened so that Nicaragua's current plans for elections Nov. 4 would not be allowed.

A high State Department official said that the governments of Honduras, El Salvador and Guatemala had "pretty much" agreed that changes were needed along the lines of the U.S. suggestions.

The participating nations are supposed to submit their final proposed changes for the treaty today, but Honduras has invited the five signatory nations to a further discussion of the pact Oct. 19 in Tegucigalpa. Mexican diplomats said they did not expect a final document to be signed this year.