Well, keeping in mind that this is probably not my most slaved-over edit ever (I cut it in a semi-all-nighter in about 3 to 4 hours for class, then touched it up for another hour before I uploaded it online), but my main focus was visual rhythm. The way in which the shots are made to interact or reflect off one another via a cut is paramount, and makes the shots used more effective.
Obviously you want to cut to beat plenty so that you anchor the visuals to the music, but by dropping off beat and letting an image run or by cutting to beat inconsistently, you can create contrast within your edit. The biggest power this gives you is that when you DO cut directly to beat, it will emphasize a part of the song.
It also helps if you are working with footage that has it's own visual rhythm, independent of editing. When I shot this, I had my DP use a jib arm and do specific types of swoops at specific speeds. I knew the song really well, so I could picture these shots matching certain undertones of the song by the way they moved, or their pace (the shots going from the ground up on Ivey, and then Ivey and I on the couch are the two biggest examples- they are slow unbroken shots that come in directly after serious beat-matching. They both mirror an undertone of the song and are made more dramatic because of it). I also had him shoot take after take after take of him searching around me and the set, moving the camera however he wanted. This gave me lots and lots of movement that I could juxtapose to create visual rhythm to complement the song, even if I didn't cut on every drum beat or whatever.
I hope this wasn't more than you were looking for, and feel free to call me on my shit if you disagree- I'm no expert.
If you have anything that you ever want critiqued, let me know. I'd love to do it, and I'll always happily hear suggestions on my own shit too.
EDIT: Most everything I mentioned I learned via instinct, reading books (Murch! Murch! Murch!) or through pure osmosis of observation. The stuff they're teaching me in school is almost purely technical- workflow, AVID tool control, etc. Directing the Narrative (which is what I made this for) is about staging and shots, so I guess there is a bit there- but not really an editing thing.
We have a Theory of Editing class that I will likely take, but it's not a subject I've had much formal training in yet.
