There's quite a bit of movie shooting scheduled around town for the next 11 days. Starting today, Paramount Pictures, television, will be filming a series pilot: "D.C. Cop." Created by Washington writer James Grady, author of "Six Days of the Condor," the series will be shot at the usual memorials, in the upper Northeast Thursday and in Georgetown Friday. On Saturday the filmmaker will be on Capitol Hill and in Georgetown again, this time under the Whitehurst Freeway.

Some key scenes, which concern the assassination of a Latin American woman ambassador, will take place tomorrow and Thursday night at the Corcoran Gallery. Grady, who wrote the script with executive producer Dick Berg, is trying to show Washington as a complex city with a competing array of sometimes conflicting police agencies. Another Washingtonian, Robert Hooks, will portray a metropolitan deputy police chief in the pilot. The lead is Cotter Smith, last seen playing Sen. Robert Kennedy in the television mini-series "Blood Feud." This time he will be an investigative newspaperman-turned-cop.

Grady is the person who could make this one work. Unfortunately, Washington never seems to come out of these film projects resembling anything Washingtonians recognize. It takes more than actors in front of the Lincoln Memorial to make a Washington story. The Family Behind the Clarinet

As that powerful group of mostly Republican leaders gathered Friday for a black-tie salute to Max Fisher, Detroit industrialist and supporter and friend of Republican presidents, the guests were generally unaware that the clarinetist playing at the reception and dinner also was well connected. The dinner was hosted by Leonard Garment and his wife Suzanne. The clarinetist was his son, Paul Garment, who has just returned to Washington after two years as principal clarinetist with the Natal Symphony Orchestra in Durban, South Africa.

The clarinet is almost a Garment family instrument. Leonard Garment also plays the instrument and helped work his way through Brooklyn law school with it. Garment points out that he is also a good friend of and once represented the all-time great clarinetist Benny Goodman. Being a dutiful father, he took his son to meet Goodman at dinner at the Bristol Hotel when Goodman was in town recently. End Notes

Sen. Carl Levin is considered one of the best squash players on the Hill and he and a number of other members of Congress play at the Capitol Hill Squash Club. Since the club was observing its fifth anniversary Friday, someone thought it would be a good idea to have the Michigan Democrat challenge someone from the House. Unable to find any takers, Levin's brother, Rep. Sander Levin, decided to take him on. Wouldn't you know it, the brothers played to a draw. In good political families, no one wins, and no one loses . . .

Both top winners in the 38th annual George Polk awards in journalism, announced this weekend, were honored for coverage in South Africa. Correspondent Ted Koppel and his executive producer Richard N. Kaplan of ABC's "Nightline" were given the award for their week-long series of telecasts from South Africa. The other award went to Alan Cowell of The New York Times for a series of dispatches and a Sunday New York Times article on the men and women behind the black struggle for equality in South Africa . . .

Swedish Ambassador Wilhelm Wachtmeister will have a Book of Condolences available for signing today through Wednesday for assassinated Swedish Prime Minister Olof Palme. The book will be at the ambassador's residence at 3900 Nebraska Ave. from 10 a.m. to 12:30 p.m. and from 3 to 5 p.m. On Friday, there will be a memorial service for Palme at the National Presbyterian Church at 11 a.m. . . .