I had a professor of a class dedicated to the history of Western music use this song to illustrate various elements of music. It took us by surprise, because it was the only foray into modern pop the class provided (which is not a complaint).
I used the lyrics in my logic class, having students look for tautologies, self-reports, imperatives, rhetorical questions, and other elements of sentence-based logic. Truly, one can use this wonderful song to explore disjunction, enthymemes, hypotheses, and so forth. One can even take the common words of the song and have students trace the origins.
One could argue that doing so may suck the pleasure out of the song, reducing it to a logical curiosity, but I found that with enthusiasm it works as an illustration of how to truly know a song, to explore it as more than just a melody.
Of course, the brilliant music can be part of the exercise. The shift in key, the shift in rhythm (the waltz beat) and other elements can be used to discuss the instinctual side of the human mind. Reason is a large part of our mental processes, but we must recognize the instinctual side of our psyche that arises as we encounter art and even interact directly with other people.
Students can also make abductive predictions about the inspiration, context, and message of the song. Because this was one of the closest collaborative products of the Lennon/McCartney team, students can be told that different lines were written by different songwriters - can they offer a guess on which? Lennon saw his contribution as pessimistic, while McCartney's were optimistic. By having the students look up those words, they can make stronger predictions about who wrote which part. They can also discuss how the music underneath the particular parts supports their educated guesses.
By using one song, the human mind can be explored in a way a junior higher can grasp.
It's also fun to watch the one rebel who says "The Beatles were overrated" as he or she is shouted down by the budding music lovers in the room who listen to more than Hannah Montana.