John W. Hinckley Jr. goes on trial today on charges of attempting to assassinate President Reagan, one year and 28 days after Reagan was shot and wounded outside the Washington Hilton Hotel.

Yesterday, as lawyers for both sides argued an array of unresolved legal and evidentiary questions, Hinckley sat six floors below, in a windowless courthouse basement cell that is expected to be his home for the duration of the month-long trial.

Extra contingents of deputy U.S. marshals and other federal security officers were evident throughout the U.S. District courthouse here, where elaborate security procedures have been put into effect in anticipation of widespread public and press interest in the case. Jury selection is scheduled to begin at 9 a.m. today. The courthouse will open at 7 a.m.

Hinckley contends he was insane at the time of the shooting and therefore should not be held criminally responsible for his acts. But Assistant U.S. Attorney Roger Adelman told U.S. District Judge Barrington Parker yesterday that psychiatrists who examined Hinckley for the prosecution do not believe he has any serious mental problem.

"None of the government psychiatrists think there is any serious mental problem with Mr. Hinckley at all," Adelman said.

His remarks came in response to a comment from defense lawyer Gregory B. Craig, who said he did not expect any dispute during the trial over whether Hinckley suffers from a psychiatric disorder. Craig said he expected the real issue in the trial to be whether Hinckley's mental illness prevented him from abiding by the law.

In other developments yesterday, Parker said he will allow government prosecutors to show the jury television videotapes of the March 30, 1980, shooting, one at normal speed and one in slow motion.

Assistant U.S. Attorney Robert R. Chapman said in court that the tapes have been edited at Parker's direction to exclude closeup views of the victims and their injuries.

Hinckley's chief defense lawyer, Vincent J. Fuller, has repeatedly objected to use of the tapes, contending they are unfairly prejudicial to his client. Hinckley has conceded that he fired the shots from a .22-caliber pistol that injured Reagan, his press secretary, a U.S. Secret Service agent and a D.C. police officer.

It was also disclosed in court yesterday that the prosecution wants to introduce into evidence a television videotape of an October 1980 campaign appearance in Dayton, Ohio, by then-President Jimmy Carter in which a man believed to be Hinckley is seen near Carter. The defense opposes use of the tape.

Parker said he will view the tape and two still photographs of the man identified as Hinckley, to decide whether it can be used as evidence.

The judge refused yesterday to change his decision to allow the jurors in the case to return to their homes each day after trial instead of sequestering them in a hotel.

Parker said the option of sequestering the jury remains available if a problem arises during the trial.

It was revealed at another court session yesterday that the prosecution may introduce into evidence a tape recording of a telephone conversation between Hinckley and actress Jodie Foster; a recording, also made by Hinckley, of an episode of the television program Saturday Night Live, in which Foster appeared, and letters he wrote to her.

Law enforcement officials believe Hinckley was obsessed with Foster and fired on Reagan to gain her attention. Information about the evidence was disclosed during arguments on a request from broadcasters, opposed by Foster's lawyers, that the television networks have access to Foster's videotaped deposition if it is introduced at Hinckley's trial. Parker has not yet ruled on the issue.

Hinckley, who has been held at the army stockade at Fort Meade, Md., was moved into the courthouse Sunday, bringing along some clothes, books and his guitar.

Provisions have been made in the courthouse cellblock over the past few months to accommodate Hinckley, who has twice attempted suicide since his arrest on March 30, 1981. Lighting fixtures with impact resistent lenses have been installed and wire mesh has been placed over the cell door to prevent access to its lock.

He is under constant surveillance by inspectors from the marshals service, and a marshals service paramedic is on duty when the regular courthouse health unit is closed for the day, according to U.S. Marshal J. Jerome Bullock.

The beige-tiled cell, which has a toilet and wash bowl, is furnished with a bunk bed, a chair and a small table for writing, Bullock said. He described the provisions in the cell as similar to those at the D.C. Jail, where prisoners are customarily held overnight during ongoing trials. The cell is 17-by-14 feet in size, Bullock said.

Food is being brought to Hinckley from a variety of places, which Bullock declined to identify, and a shower for Hinckley's use is located nearby.

Citing security concerns, Bullock refused to say "when, if, or how we are going to move him, if at all" during the trial, which is expected to last at least a month.