You didn't purify a whole state in Fallout 3
1. D.C. isn't a state to begin with
2. The Purifier is stated to ONLY purify the water in the tidal basin, aka that small lake in front of it.
And yes, the BoS make several mentions to Fallout 3, and one of the companions in Fo4 is a character from Fallout 3.
1. No, it didn't spread across the wasteland, the pure water was only that small lake in front of the purifier.
2. There IS a Washington state... but its on the WEST coast. Washington D.C. isn't a state, its a political region that sits between/in the states of Virgina and Maryland on the east coast.
They meant the DC wasteland. and Washington is a state, yes, Washington D. C. is not, they do not even have any real power over themselves, the US government pretty much rules them completely.
As for references, the BoS references the fact that Elder Lyons died (obviously), and how they fault the enclave 10 years ago (though the enclave are only called rebels)
Also, Dr. Li found a new job, and Macready from Little lamplight is a companion.
EDIT: oh, and some of the traveling merchants apparently mention that the first city from fallout 3 has expanded, which also means that they were never nuked by Tenpenny.