HOWEVER RAGGEDY morale within the government of Marion Barry has been recently, his choice of Carol B. Thompson to be second in command -- with consolidated powers denied her predecessor -- has sparked new enthusiasm throughout city hall, and rightly so. Miss Thompson has earned an excellent reputation with people in and out of government as a good manager, an independent thinker and a public administrator of integrity. Unlike Thomas M. Downs, whose authority was diminished by Mayor Barry under a strange three-deputy-mayor reorganization, Miss Thompson has won a commitment to restore the city administrator's powers to the level accorded Mr. Downs' predecessor, Elijah B. Rogers. The question now is how Mr. Barry will treat the advice he will be offered.

Though Mayor Barry insists that morale is fine, that's not exactly a universally held view in his administration -- or through the rank and file. Some of the flagging spirit can be attributed to the drawn-out investigations of the Barry administration by U.S. Attorney Joseph DiGenova, which seem to have no end in sight; some of it can be linked to Mr. Barry himself, who, according to a number of aides, has become increasingly suspicious of the people around him -- and more interested in unwavering loyalty than in the sort of challenge he used to welcome.

If Mr. Barry can tone down his cheerleading for himself long enough to entertain advice and can refrain from criticizing top aides from behind their backs, he should benefit noticeably from the counsel of his new city administrator -- whose knowledge of public administration is matched by an excellent sense of her home town and a determination to make it better.