In light of recent errors by pilots of commercial jetliners, the new head of the Federal Aviation Administration said yesterday he is planning an industrywide review of pilot training programs.

"We have seen indicators that this is necessary. We see breakdowns in pilot vigilism and pilot professionalism," said Allan McArtor said to reporters at FAA headquarters. "It is necessary to ensure that every pilot in the system is earning his wings every day."

The FAA is conducting a three- to six-week investigation of Delta Air Lines' pilot training program in Atlanta. The review began after Delta pilots were involved in incidents last month that included landing on the wrong runway, landing in the wrong city, inadvertently shutting down a plane's engines while taking off and nearly colliding with another jetliner over the North Atlantic.

"Shutting two engines down is definitely something you want to avoid, especially if you're flying a two-engine airplane," McArtor said, referring to a June 29 incident, when a Delta pilot taking off from Los Angeles International Airport almost dropped into the Pacific Ocean after shutting down both engines on a Boeing 767 jetliner. He restarted the engines and flew to Cincinnati without further incident.

McArtor said that the FAA has found no correlation between the incidents and Delta's pilot training program.

"We consider Delta to be a quality carrier," he said. "We don't see anything happening to Delta that we don't see happening systemwide."

The FAA is also investigating a near-collision at Chicago's O'Hare International Airport, where an American Airlines jetliner had to abort a takeoff to avoid hitting a Continental Airlines jetliner on the runway. Tapes of conversations between the controller and the Continental pilot released by the FAA yesterday showed that the Continental pilot had been told to take two right turns after landing, an instruction the pilot acknowledged receiving. The pilot took only one right turn, which put him in the path of the oncoming American jet.

Since taking the job six days ago, McArtor has been busy with news media appearances; he also attended the Experimental Aircraft Association air show in Oshkosh, Wis.

The former Air Force Thunderbird precision flier and Federal Express executive said he hopes to "make a difference" at the agency in the final 18 months of the Reagan administration.

McArtor said his plans include speeding up modernization of the air traffic control system and restoring the public's confidence in flying.

"There is a concern on the part of the public that the competitive pressures on airlines may bleed over into their performance in their maintenance and security programs," McArtor said. But, he added, the more the public learns about aviation, "the more confident they'll be, the safer they'll feel."