A Canadian diplomat, smiling wryly, remarked not long ago on the state of relations between Canada and the United States: "The relationship is great, except for every one of the issues."

In the past six years Canada has spent millions of dollars attempting to remove the specific irritants through an aggressive, high-profile campaign into the corridors and dining rooms of power and influence in Washington. To some of its people, Canada had appeared to behave increasingly like a U.S. special-interest lobby.

While these efforts have been widely regarded here and in Washington as effective, they have drawn Canada into another arena of modern Washington life: the public investigation.

Last week Canada's embassy in Washington found itself fending off questions from the news media and congressional investigators about the Canadian government's $105,000 contract with former White House deputy chief of staff Michael K. Deaver. Canadian spokesmen in Washington and Ottawa chafed at the prying questions.

Said embassy spokesman Bruce Phillips, "It's the policy and practice of the Canadian government not to give evidence and not to appear before the tribunals and committees of foreign governments. That has been our longstanding practice."

Canada and the United States have the world's largest trading partnership, are intimately intertwined on defense, agriculture, energy, fishing, cultural concerns and in other areas. There are nearly 70 million crossings annually of the world's longest undefended border.

But there are numerous irritants in the relationship, irritants that loom large here but at best are of only regional concern in the United States -- much to the consternation of many Canadians.

Canadian cable companies operating on the border steal signals from U.S. television stations while U.S. midwestern governors act to protect their hog farmers by blocking the export of cheaper-priced Canadian hogs. There is an ongoing struggle between the Canadian lumber industry and U.S. timber states, especially in the Pacific North- west.

The innovation of Canadian Ambassador Allan Gotlieb upon his arrival in Washington six years ago was to construct and fine-tune an operation that dug into the American political system.

It was a recognition that the old style, quiet diplomacy carried out through State Department channels, was no longer sufficient to handle all concerns.

"We have been led to adopt bold, innovative, perhaps sometimes even radical steps in the implementation of our policies toward the United States," Gotlieb told Canadian political correspondent Val Sears last December.

Sears reported back to Toronto Star readers how Canada had begun "behaving exactly like a U.S. lobby for oil, airlines or the right to carry a gun.

"Today, Canadian diplomats prowl corridors button-holing congressmen and staff. We host breakfasts in congressional dining rooms. We feed a borrowed computer with information on bills, on congressmen, on senators' wives, on polls and speeches."

The Canadian government has also been known to privately conduct polls to sample American opinion on questions not raised by U.S. pollsters.

A fund of about $518,000 for legal and consulting operations is established for the embassy, according to William Fox, communications director for Prime Minister Brian Mulroney. One knowledgeable Canadian source said last year that total lobbying operations, however, cost much more. When expenses for the huge embassy staff are added, he estimated that lobbying costs in Washington rise to about $3.5 million annually. Canadian spokesman Phillips said Friday that the figure was inaccurate but that he did not know the correct amount.

The splashiest parts of the Canadian presence in Washington have been the celebrated parties of Gotlieb and his wife, Sondra, that brought together, as she reports in a satirical column for The Washington Post, the Powerful Jobs and Serious Media of the capital's e- lite.

Guests from top echelons of the news media and the administration have long enjoyed the attention.

"The secret," Allan Gotlieb told reporter Sears, while surveying one such star-studded party at the embassy last year, "is to bring together the famous, so they can talk to each other."

But there has always been a Canadian purpose behind these gatherings. One former member of the embassy staff recalled last week how the Gotliebs courted Attorney General Edwin Meese III and developed Deaver as a pipeline to the White House when Meese went to the Justice Department.

That former staffer also said the embassy was alarmed after Deaver announced in January 1985 that he would be returning to private life. The fear in the embassy, according to the source, was that Deaver would leave before the first full summit between President Reagan and Mulroney in Quebec City in mid-March.

When Deaver stayed until May, the former staffer said, "The word in the embassy was that he stayed on because he wanted to do something for Canada."

Another Canadian source disagreed but said, as others have, that Deaver played the central role in organizing the Quebec summit and in helping change Reagan's approach to acid rain, the major irritant between the two countries.

The Washington Post, quoting a Canadian source, reported on Friday that before Deaver left the White House he discussed a business deal with Canada, to take place once he set up his consulting firm. Fox, Mulroney's spokesman, said that the allegation is "untrue."