IN AN OVAL OFFICE SET, as in life, God is in the details. ''Ours is the most architecturally accurate,'' Mr. Coates said. ''In niches and alcoves, what had been regular shelves on other sets are really coffered octagons in ours. We have sliding doors that slide -- in Warner Brothers' set, they were hinged. Joe Blow audience member may not go, 'Oh, that's wrong.' But a million visitors see the Oval Office every year.''