THE OUTSIDERS appointed to look into revelations of Soviet bugging and questionable Marine conduct at the Moscow embassy are now checking in. James Schlesinger, former chief of intelligence and defense, has proposed a plausible plan of rebuilding and new construction to fight the bugging, and Melvin Laird, also a former secretary of defense, is about to submit his report on security personnel and procedures.

Mr. Schlesinger, in Hill testimony, made plain that grievous errors of judgment had virtually invited Soviet exploitation at the American Embassy. First at fault was an attitude of seeming indifference to the whole Soviet tradition of contempt for and distrust of foreigners. Because of this attitude, the Soviets were given extraordinary opportunities to load up the embassy with bugs of a technological advancement even now beyond American matching or countering. What fools the Russians must have thought we Americans were.

The State Department is alert these days to the corrosive insinuation that if it cannot make and police an agreement on building its own house, it cannot expect to be entrusted with more demanding tasks. The department insists that it has learned from past errors and that it is now fully organized for the imperatives of embassy security. Congress will no doubt want to equip itself to keep an eye on how well the department does in building buildings and maintaining security at them -- problems which assumed proportions of scandal in Moscow but which exist for the United States in one or another degree around the world.

American alertness, however, is not enough, according to Mr. Schlesinger; Soviet cooperation is essential, too. It is foolish to expect the Kremlin to abandon its propensity for espionage, but it is essential to negotiate new construction terms that will allow the United States to protect itself adequately. The requisite leverage may be available, Mr. Schlesinger suggests, in the Soviets' desire to gain full use of their own newly constructed facilities in Washington. They may also wish to contain the outrage that they now can see Americans feel about the Soviet embassy penetrations. The Kremlin's approach to this matter will be a good test of its seriousness about improving relations with the United States.