I'd been thinking the harmonies on this sounded very unusual for the time: complex but not Beatle-esque. In figuring out the chords, though, I'm now hearing it as being more Beatle-like. If it is, it's quite an assimilation; if it's not, it's quite a feat in itself.
Perhaps the major difference is this song's big reliance on seventh (both major and minor seventh) harmonies. You hear this right away when the lead guitar climbs up from the fifth to the seventh over the tonic chord in the first seconds of the song. It is then driven home when, at the strongest possible moment for a tonic chord to be used, they instead use the tonic seventh chord on the word "sorry" in the chorus ("I'm sorry to let you down").
Very nice liaison between the verse and the chorus, making it all flow as one entity. This begins with an alternation of major and minor tonic chords, followed by a progression that uses the ii chord as a sort of sweet and wistful base to which they keep returning. (Even at the very end of the chorus, the ii chord is used instead of the dominant on the words "my side of town" before the return to the tonic.)
There's also an augmented chord in there and then the bridge uses a minor iv chord (D minor) as a pivot to modulate from A major to C major.