A number of annoying purple spots were beginning to pop up in all my photos. After a bit of Googlery, I found out that it's a hardware issue that a few people solved (without taking their phone back to Apple) by replacing the camera.
All in all, it went well. I read all the little available comments (some helpful, some not) and did what needed to be done. It was slightly OH-NO-WHAT-WILL-BECOME-OF-THIS-HORROR?! at a few points, but I succeeded in the end. Purple spots are gone.
Do all the steps. A few commenters suggested skipping most of the steps. In following all of them, I realized how easily I could have made a mistake if I'd listened to the skippers. Also, keep track of the pieces you remove. I simply took a piece of paper, and every time I took out a screw or a piece, I put it on the paper, drew a circle around it, and wrote the step number down. It was really easy to get everything back together in the end.