Vice President Mondale has faced one tricky diplomatic test on his round-the-world trip that most touring officials don't encounter. At most of his stops, including this one. He has had to figure out how to avoid the ambassador.

His problem arises from the fact that the brand-new Carter administration has not had time in its first week in office to name its own representatives to most of the major capitals Mondale is visiting.

The ambassadors are Nixon or Ford holdovers - not spokesmen for the "new era" that Mondale is telling the foreign governments is about to begin.

As he said today, "Our policy is not to include the political ambassadors . . . in the meetings, in the expectation that it might inhibit discussion of new policies. That does not apply at all to the career ambassadors, the regular Foreign Service officers."

Mondale insisted, "It's not an insult at all. They've all done fine work. We just thought it might be inhibiting, and we've indicated that to them. . . . They all understand that."

Maybe. But the finessing of the ambassadors has not been all that easy. In Brussels, for example, Ambassador Robert Strausz-Hupe is the U.S. member of the NATO Council, the body the Vice President was addressing.

He could not be excluded from the entourage. But the elderly conservative Republican, who is anxious to retain his job, was relegated to a rear car in the motorcade - a sign to the observant that he may soon be returned to academic life.

In Bonn, the next stop, career man Walter Stoessel was a full participant in the talks and is expected to remain in office.

In Rome, Nixon appointee John A. Volpe had already turned in his limousine and left town. Mondale brought Carter's choice for the Rome embassy, Richard Gardner, on the plane with him, even though Gardner has not yet been confirmed for the post.

It was in London yesterday that the awkwardness of the situation became most vividly apparent. Anne Armstrong, a former co-chairperson of the current government. He remembered a Scottish dringr in the Nixon White House, came out in a bone-chilling rainstorm to greet Mondale at the airport.

But her name was conspicuously absent from the list of those attending his afternoon talk with Prime Minister James Callaghan or the "working dinner" that Callaghan gave for Mondale and the U.S. party at No. 10 Downing Street.

British Foreign Secretary Anthony Crossland made a point at the airport ceremonies of describing the Texas Republican as "one of the most effective and popular ambassadors we have ever had here." Her opposite number, Sir Peter Ramsbotham, the British ambassador to Washington, was at the prime minister's dinner. Armstrong, who has announced her resignation, effective in March, was crossed off the American list, in conformance with Mondale's rule.

As it turned out, the "working dinner" was transformed into a rather boisterous evening. Albert Eisele, Mondale's press secretary, said, "There was no dancing on the table but there was a lot of singing and laughter."

Mondale recalled a summer he had spent in London when he attended discussions of socialism at the Fabian Society with some of the leaders of the current government. He remenbered a Scottish dringking song he had learned then, something called "I Belong to Glasgow." Callaghan promptly led the group in singing it, and Mondale proved he had not forgotten the words.

Fueled by some 1953 Mouton Rothschild wine and 1912 cognac, the diners went through a whole repertory of Welsh and Scottish songs, Labor ballads and stories. it was not clear whether Armstrong's presence would have been "inhibiting " in the sense Mondale suggested.

It was noted that the nostalgia of the evening was so strong that when Mondale went shopping in a London store early this morming, he introduced himself to a bystander as "Senator Mondale," not "Vice President Mondale."

Nor was it known what word Armstrong sent to her ambassadorial colleagues in Paris, Kenneth Rush and William Turner. Rush, the ambassador to grance, is Nixon's former law professor who served in a variety of high-level Nixon administration positions before taking up his Paris positions. Turner, a former Phoenix businessman, became one of Nixon's last ambassadorial appointments when he was named the U.S. representative to the Organization of Economic Cooperation and Development, headquartered here.

When Mondale arrived at noon for an afternoon of talks with OECD officials, preceding Saturday's meeting with French President Valery Giscard D'Estaing, neither Rush nor Turner was at the airport to meet him.

Neither was waiting when he reached the Crillon Hotel, either. Neither, it turned out, was in town.

"When did they leave?," an embassy press officer was asked.

"I believe it may have been this morning," he said. "Where did they go?"

"I'm not sure, but I believe it may have been London."

"Why? Did they have urgent business there?"

"No. Ijust think they felt their presence in Paris might have been, shall we say, inhibiting."