As much as I loathe Wikipedia as a source:
"Comments have been made over the years about the lyrics that ambiguously are either "this ever-changing world in which we live in" or "this ever-changing world in which we're living". The "in which we live in" version has been cited as being redundant and/or improper grammar. When asked about the lyrics, McCartney responded that he doesn't remember for sure himself, but that he thinks it is "in which we're living."
Listen carefully and critically to the original recording.
Methinks he decided to cover his arse with King's/Queen's English once knighted ...