Am I just slow, to not realise that an unqualified "Washington" on the radio meant the one in the eastern US?

You've been paying too much attention to Mr. Gates or Mr. Cobain, methinks.

In general, though, an unqualified ``Washington'' is going to be Washington, DC (it is the capital, after all ), except, probably in the Pacific Northwest. Any references to Washington State would be as ``Washington State''. At least in my neck of the woods.