Problems are mounting for the Transportation Department's Federal Aviation Administration in its efforts to rebuild the nation's aviation system to handle as many planes as it did before the Professional Air Traffic Controllers Organization (PATCO) committed professional suicide in August, 1981.

Proof of that has come twice in the past week. The National Transportation Safety Board reported that there have been some "safety problems" in the FAA's controller training efforts. In a letter to the board yesterday, FAA Administrator J. Lynn Helms acknowledged that some problems remain and that the agency will step up its "vigilance."

Top FAA officials also held a quiet meeting with the major airlines to outline a proposal for handling traffic at the busiest airports.

The proposal is labeled the "National Spacing Program," and is defined on one of those neat FAA viewgraphs as "a method regulating all traffic departing and arriving at designated airports by establishing timed spacing between aircraft which results in a disciplined flow of traffic."

When you cut through that, it comes down to another plan that lets the FAA control airline schedules instead of letting the market control them, the presumed goal of airline deregulation. As the Civil Aeronautics Board retreats into oblivion as the regulator of routes and rates, the FAA assumes an even more important role by regulating access.

The airlines have tolerated schedule control since the strike because they have had little choice and figured initially that it was a small price to pay to stem growing antagonism between pilots and PATCO controllers.

But it is becoming increasingly obvious that Helms will not be able to restore the system to full strength by next spring, as once was promised, so a "disciplined flow of traffic" will still be needed at the busiest airports, such as Washington National, Chicago's O'Hare International , New York's LaGuardia and Atlanta's Hartsfield.

Under the national spacing programs, airlines would submit their schedules for the busiest airports to the FAA at least one month in advance. The FAA, after massaging all the numbers, would issue a "controlled departure time" several days in advance of the flight and the airline would have to meet it. Today landing and departure slots are allotted to airplanes in a complicated lottery-like system supervised by the FAA.

The national spacing program would help the FAA smooth out the demand for peak hours (everybody wants to leave National at 8 a.m., an impossibility), and also would reduce strain on the system.

Some airlines are worried, however, that if the FAA sets schedules they will have trouble operating multiple connections at major cities. Delta and Eastern, for example, depend on connections at Atlanta to serve the south. TWA has a strong system in St. Louis that depends on many flights arriving and departing at about the same time.

"It's not a concrete plan; it's just up for discussion," FAA spokesman Dennis Feldman said. "We're saying, 'Here's the idea; what do you think about it?' " The Air Transport Association is thinking about it.

All this is related to safety, and comes down to the professionalism of the controllers and the capacity in their computers. When the safety board says that controllers who are qualified in the morning are becoming instructors in the afternoon, it indicates that the system is operating on the edge. When the FAA seeks approval for another version of the slot allocation system, it indicates that it will be a while before it is business as usual in U.S. aviation.