As it turned out, we didn't make it through that many layers. We took the South Kaibab Trail down through Kaibab limestone (lovely fossil shells), Toroweap formation, Coconino sandstone (nice tall cliffs, like the Navajo slickrock layers around Moab but with less color), Hermit formation (mostly hidden by scree) and the various layers of the Supai group (including some nice red sandstone layers with fossil imprints). We didn't quite make it down to the Redwall limestone layer (which isn't actually red, just stained red from the Supai layers above it).
The public mule rides had been suspended a month or two ago for safety reasons (we never heard the details), and we hoped that would mean a clean trail. Not so: there were still quite a few mule pack trains on the trail, and lots of mule dung everywhere. The Kaibab trail gets pretty smelly. The park's guide calls it steep, but it turns out that the difficulty in the Kaibab is mostly in its construction: most of the trail is set up for mules, so it's a stepped staircase of very loose dirt, and it's very easy to slip when stepping down from one step to the next. Walking down a normal hiking or biking trail of similar grade would have been much easier.
The "no shade" warnings are overstated. While it's certainly no forest trail, there are scrubby trees along many areas of the upper trail, and long sections are shaded by the adjacent wall. On a warmish October day, it was fairly pleasant most of the way, and only slightly hot climbing, nowhere near as brutal as we'd expected. Of course, in high summer I'm sure it's a test of anyone's endurance. The "no water" warnings are quite right, so obviously, you need to carry water and trail food.
The ground squirrels are typical national park squirrels: they'll come right up to you and sniff at your hand, or your camera, or anything you're holding out that might possibly be food. It's clear that lots of people don't take the "Unlawful to feed or approach wild animals" signs too seriously (and it's hard to, when squirrels run right up to you and sniff at your hand). They also like to run up to backpacks and sniff around trying to get in (but they don't seem very good at it).
We didn't make it to Skeleton Point, as I'd hoped; we still felt fine when we got down to  Butte, but the hour was late enough that we decided we were pushing our return time and should probably turn around. Maybe we were overly conservative. But it was a nice hike, we weren't too beat up afterward, and we had time left over to drive to  Point and catch the sunset light; so we don't really regret it.
Climbing back out wasn't the hell we expected. It's a lot easier to avoid slipping on those loose stairsteps when going uphill, for one thing, plus climbing isn't nearly as hard on the knees as descending. We took plenty of stops, both to look at views and take pictures and just to rest in nice shady places, and even so, ironically, the trip up took us less time than the trip down had. (Being chased up the limestone switchbacks by a mule train when we'd hoped to linger there and take pictures of fossils might have had a little to do with that.)
We ended up with plenty of extra time, so we decided to head over to Yaki Point before going back to the main part of the park.
At Yaki Point, the main interest seemed to be cell phone reception. A man at the overlook announced proudly to his companion, "I have reception here!" and proceeded to dial and have a conversation shouted as loud as he could possibly manage, the general outline of which went something like this: "I'M CALLING FROM THE GRAND CANYON." "THE GRAND CANYON." "I SAID I'M CALLING FROM THE GRAND CANYON. YOU KNOW, THE BIG HOLE IN THE GROUND." "THE GRAND CANYON, I SAID. I'M CALLING YOU FROM THERE. YES."
This went on for some time. The woman chatting quietly on her cell phone a few feet away didn't seem disturbed, but I couldn't take it, and decided the Raptor Watch folks looked far enough away that they might conceivably be out of earshot, so I wandered over there to see how things were going. (Lots of redtails, various other small hawks and falcons, no condors, no eagles. I'd seen a bald eagle the previous day, and lots of redtails plus a falcon (unidentified, but it had some red on it so maybe it was a kestrel even though it looked bigger) but no condors for me either. Bummer!)
Dave thought the raptor watch was totally weird. I thought that was weird: a man who does astronomy and goes to meteor showers (he used to play competitive chess, too) thinks counting migrating hawks is weird? Well, whatever. I appreciated seeing their board, to verify that all the hawks I thought were redtails really were, and that I wasn't the only one not seeing condors. I was curious about their decoy owl and about where the condors were, but I never got a chance to find out since Dave wanted to leave while other people were still asking questions.
When we got back to the overlook, Mister Cellphone was gone (whew!) and we were able to enjoy the view in peace until the shuttle arrived.
Back in the main part of the park: we made runs for several different overlooks, not realizing that the western road which used to be open is now closed to anything but shuttle buses. So we wasted some time and ended up at Yavapai Point looking at a dark canyon, worried that we'd completely missed the light. I knew we still had quite some time to go before sunset, and that the sun was hidden behind the smoke from the forest fires up on the north rim, but it didn't look like there was much hope of it peeking out. But we got lucky: the smoke cleared, the sun broke through, and we got a spectacular sunset across the canyon, followed by lovely sunset clouds in the west. And no one talking on cell phones! ("I'M WATCHING THE SUNSET OVER THE GRAND CANYON. IS THE SUN SETTING WHERE YOU ARE? SUN SET. THE SUN IS GOING DOWN. OVER THE GRAND CANYON. YES, THE SUN.")
I forgot to mention all the flash photography. Now, sometimes there's a reason for it. Fill flash for a portrait of Suzi and Billy standing in front of the Grand Canyon makes sense. But when you're just pointing out at the canyon and it's a mile down, I don't think that fill flash is really going to help a whole lot, unless your flash is a whole lot more powerful than the ones on my cameras. Apparently Dave actually said that to someone ("I don't think that fill flash is going to help") and got a smirk from a woman standing nearby, who looked like she had been thinking that for quite some time.
Monday night: the Tusayan cafe had a long line waiting ("For some reason all the rest of our staff decided not to show up tonight, so I'm it") so we tried the Yippie-Ei-O Steakhouse. Prices are high (like everything in Tusayan) but the burgers are pretty good. Dave and I exchanged glances over the book on the table of the gentleman at the next table: "What Every Woman Desires." (He was eating alone.) Some time later, though, he suddenly became self-conscious and turned the book over, so that the title was no longer visible. He may not have noticed that this put the spine, with title, facing toward us. I wondered whether he kept staring at me because he wondered whether I had noticed the book and he was embarrassed, or whether he was trying some devastating technique from its pages and was checking to see whether it was working. (Answer: Uh, better keep reading.)
What's the deal with Tusayan and cowboy themes? Somehow, when I think of the Grand Canyon, "cowboy" is not the theme which springs immediately to my mind. As Dave commented, "Cowboys never came near this place -- it was all Indians, all the time." But everywhere you go, you see Indian art but everything else Cowboy.
After dinner, we wandered around the general store, then back to the hotel to look at way too many photos from the day. ("Here's a shot of the Grand Canyon." "Mmm, nice. I bet this one's the Grand Canyon, too." "Yup. And, oh, look, here's the Grand Canyon.")
No, seriously, they were pretty, and some of those spectacular sunset photos actually did come out. But after a while, photos of the Grand Canyon do start to look ... repetitive. We made jokes about it. I'm sure we'll find some good ones to save.