When Walter first talks about trying to find his birth-mother they talk about his being born in California and so it was a closed adoption, but Walter says that with his research at the library he was able to find his "original" birth certificate. If it was a "closed adoption" the original birth certificate would be sealed with the other original files by the courts and therefore unavailable except under court order, i.e. the "closed" part of the adoption.
In the opening pan across the Seattle cityscape, you see the Kingdome in the background. The Kingdome was demolished in March of 2000.