I haven't seen the Roundabout revival of the 1940 comedy "Old Acquaintance"--which even Clive Barnes, in a one-star(!) review, calls "inexplicable"--but I think Ben Brantley puts his finger on something broader in the following critique:
Playing combative best friends of long standing, Margaret Colin and Harriet Harris share a stage and star billing in the handsomely upholstered production that opened last night at the American Airlines Theater, directed by Michael Wilson. But they are living in different time zones.
Ms. Colin comfortably inhabits the era in which the play is set; she makes the decades fall away. Ms. Harris presents the same world through the perspective of a contemporary comedian who has watched a lot of old movies; she makes a distant age look even more distant. Fans of fine-grained acting will admire Ms. Colin, while fans of diva-spoofing drag queens may well adore Ms. Harris.
Lesson: nothing makes a period piece seem more dated than trying to play the "period." Rather, as the most effective recent revivals have shown ("Journey's End," "Dark at the Top of the Stairs") nothing makes an old chestnut seem more "relevant" than pure simple honesty.
Even in such seemingly exaggerated times as Restoration London and Roaring Twenties Chicago, people still had genuine unforced emotions. Honesty is never anachronistic.