im registered in pierce county and haven't ran into any problems because of it. i kinda worried about that myself at first but i think it was just in my head (the idea of telling the local gov that i am packing). its valid for the entire state so you have nothnig to worry about when you go to eastern WA.
here is a link for you concerning carry laws in WA...it also lists the states that honor the Washington permit in case you travel out of state:

http://www.packing.org/state/index.jsp/washington