Theodore C. Lutz, Washington's new bus and subway chief, watched from the mezzanine of the Metro subway stop at Union Station as thousands of inauguration day visitors poured onto subway trains. "This is really making me a believer," he said.

For Washington's beleagured Metro transit system, yesterday appeared to have marked a new threshold. On July 4, the Metrobus system had collapsed in a dramatic display of inepititude that left thousands of holiday celebrators stranded downtown for hours.

Yesterday, however, the transit system passed the test, despite a few breakdowns, delays and some confusion.

The 10-month-old subway system even set a record. By 5 p.m., Metro officials said, the city's first subway line already had carried 57,374 passengers. The subway opened last March 24.

Tens of thousands of passengers also rode Metrobuses to and from yesterday's parade and ceremonies. In contraxt with the July 4 fiasco, the buses appeared to have run relatively smoothly, with only scattered incidents of delay and confusion.

Lutz was not the only believer yesterday.

Elizabeth Veath rode by bus from her Arlington home t watch the inaugural parade, even though she had been caught in Metro's July 4 collapse.

"I thought I'd give Metro another chance and I really didn't want to bring my car into Washington today," she said. She had no difficulty yesterday. Fifteen minutes after the parade ended, she was already aboard a bus en route home.

Washington's buses also drew praise from the mayor of Ramsey, N.J., Emil L. Portido, even though he had taken a taxi yesterday morning from his Crystal City hotel.

"All in all, I think the bus service was excellent, considering the number of people who had to be moved about," Porfido said. He rode a bus back to his hotel.

Many of the buses and subway trains charged no fare during certain periods yesterday, a matter of surprise and delight to many passengers. A woman dressed in mink was astonished at getting a free ride.

"Is it always free?" she asked as she boarded a subway at the Union Station shop. Normally bus and subway fares are 40 cents or more here.

Since the July 4 breakdown in bus service, Metro officials say they have tried to remedy many of the bus system's problems. Yesterday, key Metro officials were on duty throughout the holiday - one factor apparently responsible for the transit system's relative success.

Yet all was not roses.

One subway ride from Dupont Circle ended at the Metro Center station, at 12th and G Streets NW, when the train's brakes, according to Metro officials, got stuck.

"Ladies and gentlemen," an announcer said over the subway's loudspeaker, "we're very sorry but everybody must leave the train, please." The announcement was greeted by hoots of derision.

"Metro comes through," one woman jeered. "Let's hear it for Metro," added a man seated beside her. "At least you have a fighting chance on the street," another passenger chimed in.

Metro officials also reported delays on three other subway trains because of sticking doors.

Some bus riders, at least temporarily, were left out in yesterday's freezing cold.

Several thousand parade-goes who had parked their cars at the Pentagon's parking lot in hopes of riding free buses to downtown Washington waited for an hour or longer in icy weather before enough buses showed up to bring them in. About 35 prospective passengers gave up and walked across the 14th Street brigde.

It was unclear who was most at fault. Some of the passengers had arrived before the special bus service was scheduled to start. President Carter's inaugural committee had apparently miscalculated the number of buses that would be needed and the buses themselves appeared to have started out late.

Scattered dalays occured elsewhere during the day, including one at 15th and E Streets NW where about 300 would-be riders were reported waiting for buses at 5 p.m. The flow of buses apparently had been impeded by a throng of pedestrians, who jammed the streets.

Many bus riders also were confused by Washington's labyrinthine transit network. "Our driver didn't tell us where to pick up the bus on the way back," said Doris Caton, who had come here from Jacksonville, Fla. She had spent 30 minutes, she said, asking for directions from Metro officials on how to find a bus for Alexandria. "I got four different answers," she added.

Some automobile owned also encounted Inauguration day mishaps. City police reported towing away about 150 cars, illegally parked near the area of the parade. One of them was described as an unmarked Secret Service Car.