Iranian demands to bring the deposed shah to justice for alleged crimes raise as many potential political problems as possible legal solutions.

The initial calls for extradition of the shah to Iran from the United States have abated.Officials of the Khomeini government now say they would be satisfied with an international commission to investigate the exiled ruler.

Extradition never was a viable option, accordig to American officials, because there is no extradition treaty between the two countries. "There's simply no legal way to do it," said a Justice Department expert in international law.

There are procedures and precedents for setting up some kind of international commission at the United Nations, for instance. This would give Iran a forum for airing its grievances against the shah as part of a package to free U.S. hostages in Tehran, as some Third World countries have suggested.

But such a solution would set a "dangerous precedent", according to Erik Suy, undersecretary and legal counsel at the United Nations. In a phone interview from New York yesterday, Suy noted that previous U.N. sanctioned inquiries into alleged misconduct by Chile, Israel and South Africa focused on "existing" conditions, not past conduct.

"If you set up a committee to investigate things [the shah allegedly did] in the past you could name 40 other countries such a committee could fruitfully examine," he said. "The difficulty is the next day someone would ask, What about Pol Pot or Idi Amin?" He was referring to controversial leaders in Cambodia and Uganda.

Suy said any such move by the 152 member nations of the U.N. General Assembly would be "a purely political exercise with a view toward activating world opinion."

Any talk of investigation is premature, according to U.S. officials. "We'll be willing to listen to the Iranian authorities' coments and complaints about the shah after the hostages are released," a State Department official familiar with the situation said yesterday. "The forum is an open matter. We're simply not looking down the road that far yet. Our only concern now is getting our people out of there safely."

The official didn't reply specifically when asked whether theU.S. delegation at the United Nations was exploring the investigating commission idea as part of a deal to free the hostages. "Various American officials are looking at various aspects of the Iranian situation," he said.

Louis Sohn, professor of international law at Harvard University, said yesterday that setting up a U.N. investigating comission would provide "an institution where Iran could take its grievances against the shah. It could but much more international pressure on them to release the hostages."

Sohn said that such a U.N. commission would be like a grand jury. Its final report could be like an indictment, he added, and then the U.N. General Assembly conceivably could pick a body of jurists to judge the matter. This has never been done before at the United Nations, he said.