"Christmas in Washington," the NBC special Sunday night at 10 on Channel 4, is an exceedingly agreeable and innocuous hour of seasonal music taped Dec. 9 at the National Building Museum here. Through the magic of stock footage, the opening title tune is accompanied by shots of the capital under a blanket (or two) of snow. No cause for alarm; these scenes were taped in a previous year.

President and Mrs. Reagan attended the event, and the president is, naturally, part of the finale. He makes a few remarks and introduces Danny LaBoccetta, the 9-year-old whose drawing was chosen for the 1984 Christmas stamp by the post office. Reagan does these things soooo well, and surely no president, at least no president alive in the age of photography, ever had more Christmasy cheeks.

Earlier, NBC News chief political correspondent Roger Mudd contributes to the program a TV news report as it might have sounded about 2,000 years ago. The birth of Jesus is not reported, but there is an item about the census, and an innkeeper who sent two prospective guests out back to a stable, sandwiched between the political poop and the weather report. Mudd was originally slated to read from the 1897 essay, "Is There a Santa Claus?" The change in program seems wise.

Others participating include Hal Linden, Nell Carter, Frederica von Stade of the Met, and the Osmonds, including Donny and Marie, whose thin, dull voices sound thin and dull as ever. Eventually there are seven Osmonds on the stage, all of them seeming to share in one tiny talent stretched to the breaking point. Donny sings "White Christmas," or rather, "Oooo, I'm dreaming of a white Christmas."

The Naval Academy Glee Club and the Shiloh Baptist Church Choir also participate and make joyful noises. Most of the songs are of the secular holiday sort; a medley of carols ends the program. There is no shot of the nativity scene on the Mall, but President Reagan joins in the singing of the concluding "Hark, the Herald Angels Sing."

Nancy Reagan shows off a gingerbread house made for Children's Hospital (for whom this event was a benefit) during a brief sequence taped earlier in the State Dining Room of the White House. She does a fine job of this but seems to be walking somewhat unsteadily. Among those glimpsed in reaction shots during the performance are Supreme Court Justice Sandra Day O'Connor, White House press secretary James Brady, and NBC chairman and chief executive officer Grant A. Tinker.

Secretary of Defense Caspar Weinberger, seen during the singing of Mozart's "Allelujah" by von Stade, has a pugnacious scowl on his face that makes him look just like Willy the Warhead. But otherwise, the holiday spirit seems fairly pervasive, and the building interior photographs beautifully. Maybe next year NBC will shell out a few more bucks so as to snare some higher-firmament stars for the show. But this will do for now.