All right--possibly against my better judgment, I decided the only way to find out what's what with 12.4 was to test for myself on my system, so I bit the bullet and upgraded. tl;dr: end verdict? ...These drivers work fine for me.

Longer explanation: my AMD card is a 6970 2GB, stock speeds and a custom fan profile run through MSI Afterburner 2.2.0. Everything in the CCC is set to let applications decide except for Vsync, which is always on, and Tesselation, which is set to AMD quality. I do not use CAP profiles.
For Skyrim itself: I run the game in windowed mode, 1440x800 resolution. Everything is set to Ultra except for shadows, which are on medium with a few ini tweaks. I do not use the HD texture DLC, but I do use a few other texture mods. Nothing too fancy. 8X AA, 16X AF, FXAA on, water set to reflect everything.
For installing the driver, I did my usual method. I disabled MSI Afterburner, then express uninstalled all AMD software (I have an Intel CPU, obviously; if you have an AMD-based one this is a terrible idea) via the Catalyst Install Manager. Let that do its thing. Rebooted, then installed 12.4. Reboot again, then turn MSI Afterburner back on. Everything went as normal there, for the record.
Then it was time to launch Skyrim up and get down to testing. For this, I launched Fraps for the first time in ages to get a more accurate feel for what was going on with FPS and so on. I also had a list of stuff I wanted to check out, since people had been reporting various issues in certain spots. I played the game for about 20-30 minutes...started in Honeyside, in Riften. I ran around Riften a bit, then fast traveled to Whiterun. Ran around Whiterun a bit, then fast traveled to Blind Cliff Cave (near Markarth). Ran around a bit there, both inside the dungeon (to test out combat) and out, and then jogged to Markarth and ran around Markarth a bit. Here's what I found:
- random texture corruption and triangles everywhere (reported by Raen Yrtham): not evident at any point throughout my testing. I saw no texture corruption whatsoever.
- z-fighting (flickering on distant mountain LOD) still present: check. Engine issue. Moving on.
- severe drop in performance/FPS: not evident. I had 58-60FPS pretty much throughout, even in combat with dragons and multiple Forsworn, with a few exceptions I'll go into below.
- FPS drop only when turning while walking/running: not evident.
- game freezing/crashing when casting lightning spells (reported on the AMD forums): not evident.
- game crashing, hard freezing, BSODing, etc: not evident, although obviously I'll need to play for more than 30 minutes to be absolutely sure. Fairly confident this won't be an issue however.
- I feel like I saw more obvious shadow pop-in, particularly while in Blind Cliff Cave. This may just be my imagination however.
- FPS drops when standing in the fabled "FPS kill zones" of Whiterun up by Dragonreach and just...Markarth:
evident. In that magic spot in Whiterun I got dips down to 45FPS; in Markarth I saw as low as 37FPS at one point. However, it's worth noting that: I've never tested the Whiterun FPS kill zone extensively, and I literally have not been to Markarth in months. Game time and RL time. I haven't been there since prior to the optimizations we got in the 1.4 patch. So I cannot say with 100% certainty that those FPS drops are new and caused by 12.4. Also it's worth noting that, again, I'm not experiencing FPS drops anywhere else. Everywhere except the "FPS kill zones" is a pretty steady 60FPS.
So, that's what I've found out so far. I'll keep testing, of course. I intend to play more Skyrim tonight along with a couple of other games, like TF2. If I find anything that's deal-breaking I'll of course report back, but for now...I can't really say I see anything egregiously wrong with these drivers on my system. YMMV, but that's just what I've found.