The George Hyman Construction Co. has signed a $10 million-plus contract with George Washington University for work on the university's National Law Center. The project, designed by Keyes Condon Florance, is on 20th Street NW between G and H Streets just behind "Red Lion Row," at 2000 Pennsylvania Ave NW. It consists of two new buildings, a five-story addition to Burns Law Library and a four-story addition to Stockton Hall, and then renovation of Burns and Stockton themselves. Work is expected to be complete by August, 1984 . . . The Smithsonian Institution has retained Wagner-Hohns-Inglis of Mt. Holly, N.J., to coordinate scheduling of the first segment of the renovation of the Arts and Industry Building on the Mall. Plans call for a major ''historical exterior renovation,'' including masonry reconstruction and replacement of the roof, windows, woodwork and other fixtures to return it to its original decor. The building was built in 1881. The work is expected to take four years . . . The Prince George's County Board of Realtors will offer a three-hour seminar Monday on property inspection and water and energy conservation. The program is designed for real estate licensees.The fee is $6 for members, $16 for nonmembers. For information, call 350-7700.