The personal peccadilloes of two prominent Greeks have managed to put further strains on the always touchy relations between Athens and Washington just as the Reagan administration is preparing to renegotiate the leases on U.S. military bases in Greece.

The two are Andreas Papandreou, the Socialist prime minister and U.S.-basher, and George Koskotas, publisher of the conservative opposition newspaper Kathimerini. American officials are at odds with both of them.

Papandreou has reportedly separated from his American-born wife, Margaret, and is rumored to be having an affair with a woman named Dimitra Liani. The scandal has been given exhaustive coverage in the Greek press and has outraged both the pro-American element in Greece and the powerful Greek Orthodox Church leadership.

As Koskotas' newspaper editorially gloated over the stew Papandreou was in, the conservative publisher suddenly found himself in a mess. He was arrested in the United States on Oct. 8 by the Internal Revenue Service, just before he was due to visit the White House as a guest of the United States Information Agency. The circumstances of the arrest were embarrassing to USIA and the Reagan administration, to say nothing of Koskotas.

Apparently, USIA had not conducted background checks on the distinguished foreigners it invited to the agency-sponsored "International Council Conference." The guests included the Greek publisher, who is also owner of the Bank of Crete.

Because the conferees were to visit the White House, the Secret Service did its usual checks and found an outstanding 1980 warrant for Koskotas' arrest on 64 counts of tax fraud. The Secret Service alerted the IRS, which arrested Koskotas. At his Oct. 15 arraignment, bail was set at $1 million.

Our reporter Gary Clouser has reviewed the arrest warrant and indictment and has interviewed Elliott Jacobson, an assistant U.S. attorney in Manhattan who was involved in the case.

The indictment charges that Koskotas and three others collected unemployment benefits and income-tax refunds by creating fictitious employes of painting firms operated in Manhattan by Koskotas' father.

In addition, U.S. and Greek authorities are suspicious of Koskotas' claim that he lost his passport, and of his efforts to obtain a new one. From the Greek consulate here, he obtained a travel document to replace his passport. Prosecutor Jacobson said the passport was seized during Koskotas' arrest, and was returned to him as part of the bail arrangement. Koskotas returned his travel document to the Greek consulate and reported that he had found his passport.

A Washington-based Greek journalist, Elias Demetracopoulos, once an ace reporter for Kathimerini, tipped us to Koskotas' tax problems last January, two months before Koskotas bought the newspaper. But the IRS refused to confirm or deny the allegations. Demetracopoulos said he is upset over his old paper's "most regrettable fate."

Koskotas is a mystery to most Greeks, who are suspicious of his wealth and political clout. Meanwhile, U.S. policy-makers wonder how these personal scandals will affect relations with Greece.