The Supreme Court agreed yesterday to decide whether a police officer without reason to suspect any wrongdoing can stop an automobile to check the operator's permit and vehicle registration.

Opening their 1978 term, the justices granted a petition by Delaware to review a ruling that "a random stop in the absence of specific justifying facts is unreasonable and unconstitutional."

Richard R. Weir Jr. Delaware's state attorney general, said the ruling denies to police "the most effective method" of enforcing driver-licensing and vehicle-registration laws.

Arguing that day-to-day law enforcement everywhere would be adversely affected if the ruling were to stand, Weir said the state's interests outweigh the "minimal inconvenience of random stops." Consequently, he said, the stops are "constitutionally permissible."

The case began in November 1976, in Wilmington, when New Castle County Police Officer Anthony Avena, during a routine patrol, stopped a car to check the driver's permit and registration. He had seen no equipment or traffic violations or erratic or unusual driving.

Avena has testified that on approaching the car he smelled what seemed to be burning marijuana and then found a bag of the substance under a seat. He arrested the driver, William J. Prouse III.

The issue was whether Avena had made an unreasonable search in violation of the Constitution. If he had, the bag - the evidence indispensable to a prosecution of Prouse for illegal possession of marijuana - would have to be suppressed.

In a ruling that exempted roadblocks or other systematic traffic checks. Superior Court Judge Joseph T. Walsh found "no legal sanction" for an "arbitrary" and "capricious" stop of the kind involved in this case.

Upholding him, the Supreme Court of Delaware found intolerable the conferring of "absolute discretion and authority . . . upon the police to detain whomever they desire for whatever reason on the pretense of a documents check stop."

Last December, the U.S. Supreme Court upheld a conviction based on police discovery of a concealed weapon on a motorist - but he had been stopped for driving with expired license plates.

In a Michigan case yesterday, the court agreed to review a decision invalidating, for unconstitutional vagueness, a Detroit ordinance authorizing a police officer to arrest a person who, after behaving in a way that "warrants further arrest for criminal activity," refuses to provide and verify identification.

The court took other actions:

Hypnosis

The court let stand a first-degree murder conviction obtained with the aid of a prosecution identification witness whose memory purportedly was jogged by hypnosis.

Hypnotizing of witnesses is highly controversial. Generally, courts bar testimony obtained under hypnosis. This "seems eminently appropriate, in view of the case with which even trained psychiatrists or psychologists are misled," says Martin T. Orne, a University of Pennyslvania psychiatrist internationally recognized as an authority on hypnosis.

In a brief filed in the case, Orne told of "age progression" hypnosis, in which a person, told it is the year 2000, will provide "a vivid and compelling description of all kinds of new, as yet unseen, scientific marvels."

The case came from Santa Barbara, Calif., where, after two mistrials, a third jury convicted John P. Quaglingo of the murder of his estranged wife, Dyanne, in 1975. He was sentenced to life imprisonment.

While Dyanne was jogging, she was struck and killed by a hit-and-run vehicle that left unusual skid marks. Sheriff's officers located the car. They also found that before the accident, a man named Myron Jensen had sold it to a "Richard W. Bellmore," who then returned to Jensen to complain about the battery.

Shown a 12-year-old photo of Quaglino, Jensen said it "rang a bell." After hypnosis by psychiatrist Frank Gott, Jensen recognized "Bellmore" as Quaglino by picking out his photo from among seven of bearded men - something he had been unable to do before hypnosis.

In his own defense, Quaglino testified he had never seen the hit-run car and that at the time of Dyanne's death he was at home in bed with his friend Sonia Gowda. Initially, she said he hadn't left; later she said he had gone out to jog but he wasn't breathing heavily when he returned. The conviction was upheld by the California Court of Appeal.

Juror Infatuation

The court let stand the perjury conviction of New York Police Detective Dennis W. Mulligan although juror Virginia Stephenson, during the trial, became infatuated with the prosecutor and, in two days of deliberations, was the lone holdout for conviction.

Wiretapping

In a stolen goods case from New Jersey, the court agreed to decide this issue: when a judge authorizes federal law enforcement agents to wiretap, can they, without telling him or getting his approval, break into an office in order to install, maintain and remove electronic listening devices?

Federal Detention

The court granted a Justice Department petition to review a ruling that it must show a "compelling necessity" for every "restriction and deprivation" on persons held in federal custody pending trial.

Firearms

The court agreed to review the constitutionality of a New York law that makes the presence of a gun in a car presumptive evidence of possession by all of the occupants.

Parole

The court granted a petition by Nebraska to review a decision that the constitutional guarantee of due process of law governs the granting or denying of paroles.

Corrupt Legislators

The court let stand the mail fraud and extortion convictions of three Illinois state legislators and the extortion and conspiracy convictions of the Democratic chairman and senior Republican member of a state senate committee formed to investigate construction-cost overruns.