The Supreme Court was asked yesterday to give police "room for some mistakes" by relaxing the controversial "exclusionary rule," which bars illegally seized evidence from criminal trials.

Illinois Assistant Attorney General Paul R. Biebel Jr. asked the court to establish a "good faith" exception to the 69-year-old rule: illegal evidence would be allowed when authorities could show they did not know it was illegal.

The exclusionary rule has become a symbol for many conservatives who believe there is an imbalance in the criminal justice system that lets criminals off on technicalities. Legislation has been introduced in Congress to create a good-faith exception.

But many groups, including the American Bar Association, support the strict application of the exclusionary rule, saying that it is the only effective deterrent to police abuse in searches and seizures.

The debate over the rule's application is considered one of the most important criminal justice disputes to come before the court in the last 20 years.

The case began on May 3, 1978, when police in Bloomingdale, Ill., recieved an anonymous letter alleging that Susan and Lance Gates "make their living on sellng drugs." The letter said that the couple had more than $100,000 worth of drugs in their basement and soon would be traveling to Florida to obtain more. Authorities verified the couple's address and, with the help of the Drug Enforcement Administration, located the couple in Florida, where they were placed under surveillance.

While the Gates were returning to Illinois, police obtained a search warrant for the couple's home and car. On May 7, when the couple returned home, police conducted the search and found 350 pounds of alleged marijuana in the trunk of their car and more in the house, along with weapons, ammunition and drug paraphernalia. The couple was indicted on drug charges.

But before their trial an Illinois judge, in a ruling subsequently affirmed by the state's supreme court, ruled that the search warrant had been invalid because it was based on an anonymous letter. Under the exclusionary rule, all the evidence seized from the couple's car and home was declared inadmissible at trial. Illinois appealed to the U.S. Supreme Court.

If the Supreme Court upholds the "good faith" exception to the rule sought yesterday, the evidence could be admitted because the police thought that they had a valid warrant.

"There is no evidence that the police acted in a willful, negligent way," Biebel told the justices. "Their action can only be characterized as thorough and professional . . . . This is clearly not the kind of police activity the exclusionary rule was meant to deter."

His argument was supported on behalf of the Reagan administration by Solicitor General Rex E. Lee.

"On the cost side," Lee said, "highly relevant and probative evidence" was excluded, damaging the "judicial integrity" of the legal process. "On the benefit side, it is difficult to see anything that would be deterred. The police obtained the warrant . . . . They did what they should have done."

No one argued yesterday that the police had done anything wrong. This is why criminal law experts viewed the case as the perfect test of the exclusionary rule, first enunciated by the court in 1914.

The problem, it was conceded, was with the magistrate who issued the warrant based on the anonymous letter. The Fourth Amendment to the Constitution says that "no warrants shall issue, but upon probable cause" for believing that they will produce evidence of a crime.

Justice Sandra D. O'Connor, whose vote is crucial for opponents of the exclusionary rule, asked how could the courts then deter "improper or even flagrant decisions by magistrates?"

"Under your view," she told Lee, "that would be perfectly all right."

"Not perfectly . . . ," Lee started to say before being interrupted by O'Connor.

"Perhaps there is a secondary motive for the exclusionary rule ," she said. "Perhaps it's to make sure" that the government as a whole, and not just the police, "doesn't engage in misconduct."

Justice John Paul Stevens picked up the theme.

"How do you deter magistrates," he wanted to know. " . . . Are you saying it's all right for magistrates to issue warrants on less than probable cause?"

The Gates' lawyer, James W. Reilley, also addressed this issue. Application of a good-faith exception in this case, he warned, "will immunize the warrant process" from review by courts. Reilley added that it would "establish a lesser standard for warrants" than the Constitution requires.

Reilley avoided the merits of the case almost entirely yesterday, while appealing to the Burger's court's sympathy for states' rights. He told the justices that the Illinois courts based their decision on state law and state court rulings and that the Supreme Court should not even be reviewing it.

While procedural, this argument has proven effective in other cases in attracting votes from conservatives.

Yesterday was the second time the court has heard Illinois vs. Gates. In the first oral argument, in October, the "good-faith" exception was not an issue. The court specifically asked to have the case reargued on that point. This was an unusual action that required five votes and signaled the likelihood of a favorable ruling from a majority of the justices.