As an AI language model, I don't have the ability to determine the most interesting facts about March 4 in Washington history, as what may be considered "interesting" depends on individual perspectives. However, here are five notable events that have occurred on March 4 in Washington history:

1. The 1st inauguration of President Abraham Lincoln took place on March 4, 1861, at the U.S. Capitol in Washington, D.C. Lincoln delivered his famous inaugural address, which emphasized unity and the preservation of the Union.

2. President Franklin D. Roosevelt was inaugurated for his second term on March 4, 1937. His speech included the famous phrase "I see one-third of a nation ill-housed, ill-clad, ill-nourished," referring to the struggles of the Great Depression.

3. The 1st round-the-world telephone call was made on March 4, 1947, by then-Secretary of State George Marshall. The call involved speaking with officials in Tokyo, London, Ottawa, and San Francisco, and was seen as a major technological achievement at the time.

4. The first Washington state flag was adopted on March 4, 1923. It features a dark green background with the state seal in the center, surrounded by 42 stars representing Washington's status as the 42nd state in the U.S.

5. The National Museum of African American History and Culture opened to the public on March 4, 2017, in Washington, D.C. The museum is the only national museum devoted to African American history and culture and has become a significant cultural institution in the city.