Animated trio of one-acters -- and some not-so-private lives; Buried Inside Extra Play by Thomas Babe. Directed by Joseph Papp.

It is 3 a.m. in the city room of the Times-Record, a Midwestern newspaper about to print a final edition before being closed down for unprofitability by its owner-publisher. As the alcoholic editor (Hal Holbrook) and his girlfriend (Dixie Carter), the woman's page editor, share reminiscences and recriminations, word comes from an anonymous telephone caller that a nuclear device has been hidden in one of the building's bathrooms.

Thereafter, Thomas Babe's ''Buried Inside Extra,'' at Public Theater/Martinson Hall, divides its attention between the personal histories of the stranded staff members and the threat of an imminent nuclear blast. Considering the possibilities, Mr. Babe manages to generate scant human interest or dramatic excitement.

Under Joseph Papp's direction, five estimable actors make what sense they can of the play's often nasty confrontations, muddy reflections, and riddling rhetoric. If there is a deeper message in ''Buried Inside Extra,'' it remains buried.

In addition to Mr. Holbrook's soddenly garrulous editor and Miss Carter's tart-tongued woman journalist, the cast includes Vincent Gardenia as an oddly eccentric assistant editor, William Converse-Roberts as an abrasive young reporter, and Sandy Dennis as the unfaithful editor's wan but knowing wife. Mike Boak's scenery and Ralph K. Holmes's lighting emphasize the metallic, gray-and-green color tone that characterize the drab decor of many a news room.