I always THOUGHT there was a mistake in this song and I was correct. The reason why it was written is intriguing. Musical beds!
From Wikipedia:
One of three songs co-written by the two male members of the group (the others being "Got a Feelin'" and "For the Love of Ivy"), "I Saw Her Again" was inspired by Doherty's brief affair with Michelle Phillips, then married to John Phillips, which, combined with an affair between Michelle Phillips and Gene Clark of The Byrds,[5][6] resulted in the brief expulsion of Michelle from the group.[7] While mixing the record, engineer Bones Howe punched in the coda vocals too early, inadvertently including Denny's false start on the third chorus ("I saw her..."). Despite attempting to correct the error, the miscued vocal could still be heard on playback. Producer Lou Adler liked the effect and told Howe to leave it in the final mix.[8]
Lou Adler has said that this song was specifically done to try and capture the flavor of what the Beatles had been doing, and that it was intentionally written to be a single.