Can a judge bar the public and the press from an entire criminal trial?

Are transcripts of Henry A. Kissinger's White House and State Department telephone conversations -- monitored and transcribed at public expense -- "personal papers" exempted from disclosure by the Freedom of Information Act?

Do policement hunting homosexuals in public restrooms violate personal privacy by peering into closed stalls from attic hiding places?

Can Congress set aside a portion of public works grants for "minority" businesses?

Can a state deny drivers' licenses to qualified applicants whose religion forbids them from being photgraphed?

These questions are among those raised by the more than 4,000 cases that the Supreme Court is to dispose of during its nine-month term, which open Monday.

Only a small proportion of the cases raise questions of constitutional or legal importance, or are simply interesting. The bulk are unimportant, redundant, absurd, instruments of delay or numbingly dull, even if perceived otherwise by litigants, specialists, cognoscenti, and lawyers who sometimes collect fees from clients gullibly expecting their causes to receive grave consideration in the great marble palace on Capitol Hill.

At 10 o'clock Monday morning after a brief ritual in which Chief Justice Warren E. Burger will open a term of the court for the 11th time, he will release an order disclosing the fate of nearly 1,000 cases.

The order will show that the court threw out most of the cases without comment. The same unceremonious fate awaits most of the hundreds of cases carried over from the last term as well as the thousands more that will have been filed by time the court recesses in late June or early July 1980.

Discarded mainly are cases in which fewer than four justices vote to review a decision by a lower federal or state tribunal.The most important survivors are the cases on which the justices will hear oral argument and decide with full opinions. There were 153 such survivors in the last term.

The mood of the court doesn't appear to be particularly cheerful.

One reason for the sense of malaise is the lingering memory of the windup of the last term, when disquiet, disarray and tensions were manifest in some of the opinions and palpable in the court's chamber.

One of the most openly divisive cases posed the issue of whether a judge could close a pretrial criminal proceeding to the public and press. He could, because the Sixth Amendment is exclusively for the benefit of the accused. Justice Potter Stewart wrote for the 5-to-4 majority. But, Stewart went on to say, the judge also could close the subsequent trial.

This assertion not only openly fragmented the majority at the time, but also, over the summer, produced an extraordinary sequel: no fewer than four justices made off-the-bench (and inconsistent) statements as to what the court really meant in its so-called Gannett ruling.

Now, if the justices grant review in a Richmond case, in which a judge excluded the public and press from a two-day criminal trial, they will have a chance to explain.

Certain other cases previously accepted for argument and decision cannot help but have significant repercussions no matter how deceded.

One example is the question: "Can Congress set aside a portion of public works grants for 'minority' businesses?"

In terms of impact on affirmative action, the case is probably less important than those in 1977 of Allan P. Bakke and in 1978 of Brian F. Weber. They were whites barred by minority quotas from, respectively, a medical school and a voluntary in-plant craft-training program set up under a union contract (Bakke won, Weber lost).

The case may, however, hold a potential to abrade the relations between blacks and Jews that were made tense by the resignation of Andrew Young as ambassador to the United Nations.

The case involves a provision in the Public Works Employment Act of 1977 for a set-aside of 10 percent of each grant for enterprises at least half owned by citizens who are "Negroes, Spanish-speaking, Orientals, Indians, Eskimos and Aleuts."

The provision, never considered by a congressional committee, but instead sponsored on the House floor, was attacked by employers and found invalid by some courts. But, in the case to be reviewed, the set-aside was upheld by the 2d U.S. Circuit of Appeals as not in conflict with the ban in the Civil Rights Act of 1964 on discrimination against "any person."

Because the $400 million at issue long since has been appropriated, the Justice Department argues that the case is moot.

While most Jewish groups have stayed out of the case, the Anti-Defamation League of B'nai B'rith, in a friend-of-the-court brief, denounced the provision with a brief comparing it with Nazi laws defining a "Jew" and with South Afrecian laws defining "white," "black," "colored" and "yellow."

The set-aside is based on "a grab-bag of purported racial, ethnic and language classifications," the brief charged. "It involves the federal government in the imprecise and dirty business of fitting persons -- and enterprises -- into racial and ethnic categories. . . ."

Obviously without regard to cases yet to be filed, here are some of the questions confronting the court. (Each question is followed by the answer of the lower court.)

Freedom of Religion

Can Colorado deny drivers' permits to qualified applicants whose religious beliefs forbid them to be photographed? (Yes)

May a clergyman who is also a public official be compelled to answer questions by a grand jury without a judicial balancing of the state's needs against his obligations as a cleric? (Yes.)

Freedom of Information Act

Under the FOIA were transcripts of Henry A. Kissinger's White House and State Department telephone conversations exempt "personal papers," although prepared by government secretaries? (No.)

Rivacy/Fourth Amendment

Do Virginia state troopers, enforcing antisodomy laws, impermissibly violate privacy by peering into closed toilet stalls from hiding places in the attics of public restrooms? (No.)

Can police with probable cause to believe a person has committed a crime make a forcible, warrantless entry into a home to arrest him? (Yes.)

Slavery

Does Alabama violate the constitutional prohibition of involuntary servitude by forcing but inadequately paying attorneys to represent indigents charged with crimes? (No.)

Freedom of Speech

Does New York State deny free speech to a public utility by forbidding it to enclose propaganda on controversial public issues in the envelopes in which it mails bills? (No.)

Can federal courts enforce a requirement in a CIA employment contract, agreed to by an employe at the time of hiring, that he had to get agency approval to publish information about it? (Yes.)

Immunity of Officials

Does the attorney general have a right to appeal a federal jude's contempt finding? (Yes.)

Were the savage rapes by intruders of a teacher who was alone in her classroom work-related, immunizing her employer from a damage suit? (Yes.)

Cruel and Unusual Punishment

Was a mandatory life sentence, imposed under a Texas habitual-offender law, unconstitutionally cruel to a man who, over a nine-year period, had been convicted of three crimes -- trying to defraud with a credit card, passing a bad check and promising to fix an appliance -- that would have netted him a total of $229.11? (No.)