The Diplomatic Relations Act passed by Congress earlier this week, and now on the president's desk, has been hailed by many as a major step toward making foreign diplomats here legally accountable for their actions. But at the same time the legislation has opened up an array of legal problems for both the diplomatic corps and residents of the Washington area that may take a long time to resolve.

For some people - victims of past accidents caused by embassy personnel - the bill offers little new hope. Although it may well help to solve parking and traffic problems generated by diplomatic cars, the Soviet Embassy, which traditionally has been the worst offender in this regard, stands a good chance of being able to continue ignoring the city's parking regulations.

Much of the congressional support for the bill came about after an accident involving Dr. Halla Brown more than four years ago. The car in which she was riding was smashed into by the Panamanian cultural attache and Dr. Brown has been a quadraplegic since. Though the Panamanian government eventually voluntarily gave Brown $100,000. her medical expenses already are three times that figure and her personal and professional losses immeasurable.

Because the attache was protected from civil and criminal litigation by his diplomatic immunity, Brown had no legal recourse against him. He did not carry liability insurance, but, even if he had, the insurance company might have used his immunity to escape payment - a common practice in other, similar cases.

The new bill will repeal a 1970 law that effectively gave everyone who worked at an embassy from the ambassador to the chauffeurs, complete immunity from civil or criminal prosecution.

Instead, it adopts the rules of the 1961 Vienna Convention, which makes embassy personnel more or less accountable according to their rank and official duties.

Furthermore, the legislation requires all embassy personnel to carry liability insurance in accordance with guidelines to be set by the president. It also would make it impossible for an insurance company to avoid payment by using the diplomat's immunity as a defense.

Because the statute of limitaions has run out, the new bill comestoo late to help Brown, and even if the new law had been in effect at the time of her accident, the Panamanian diplomat himself would not have been touched.

Because of his rank he would be among the approximately 7,000 diplomats and their families here who remain immune to criminal prosecution, and subject to civil action only in a limited number of cases.

Under the new regulations the approximately 2,900 members of embassy technical and administrative staffs here also would retain full immunity from criminal prosecution and would be immune from civil suits only when acting in official capacities. Their 7,000 family members would have no civil immunity.

Embassy chauffeurs, janitors and other service personnel - about 270 in all - would have civil and criminal immunity only if they acted at embassy direction.

But, as a spokesman for the Nigerian embassy said, "This is a very difficult thing to know, whem somebody is on duty and when somebody is not on duty."

The area where all these questions most commonly come into play is on the city's streets. Last year it was estimated by court officials that 80 percent of the parking tickets given to cars driven by embassy personnel were unpaid, costing the city an estimated $1,070,000 in lost penalties and fines between January 1976 and April 1977.

The worst offender was the Soviet Embassy, which received 12,270 tickets.

People in Congress and the State Department familiar with the new law, however, believe that the Russians may be able to circumvent it. Because of fears on the part of U.S. officials that U.S. embassy personnel in Moscow might be subject to legal harassment if not given full immunity extended well beyond the bounds of the Vienna Convention, the U.S. and the Soviet Union have in the past come to their own special reciptrocal agreements.

There is a provision in the new law to allow the president to continue with the same policies, and congressional and State Department sources believe that he will.

Another area of constant friction has been in business dealings, where leases and contracts were broken by embassy personnel immune to suit. On this score, there does appear to be a major change, since the Vienna Convention does not exempt even ambassadors from such civil actions.

Virginia Schlundt, counsel to the House subcommittee on international operations, said she was aware of the legal questions left unanswered by the bill. "We're going to be have a bunch of lawyers arguing on the basis of the Vienna Convention and digging into experiences with it from around the world," she said.