This is almost certainly not a bug in Steam. I noticed that the android emulator shows exactly the same problems.
I guess it's a problem with AMDs drivers and possibly some configuration issue with my machine. Maybe the 12.12 (13.1?) release fixes that. (Hopefully Ubuntu makes the 12.11 beta fglrx version available via repos soon!)
In case anyone has the same problem and finds this bug report, this is how I solved it:
In KDE system settings, go to "Desktop Effects" in the "Workspace Appearance and Behaviour" section. Open the "Advanced" tab. Change "Compositing type" from XRender to OpenGL.
I was pretty sure that steam had worked with my new KDE setup for some time, even though XRender apparently is the default setting and I never (knowingly) changed it. Now even glxgears (ANYTHING that needs opengl) will refuse to redraw when XRender is enabled.
Anyway, definitely not a steam bug, sorry for the noise!
Nothing extracted yet.
The steam client fails to update its UI for me recently. That means I click a button or type text into an input box, but it seems like nothing happens at first. Then, when I move the steam window or go to a different window and switch back to steam, the UI is updated with the new page or the text displayed in the input box. This happens for example with the username/password input fields for logging in.
The only exemption is the menu bar. Clicking e.g. the "Steam" menu (upper left corner) opens the menu instantly, but the blue background that highlights the menu entry where the mouse cursor is currently hovering fails to update as I move the cursor through the menu.
It used to work fine earlier, and AFAIK there was no steam client update since then. I suppose it's some third-party package that I have installed or upgraded recently. For example, I've installed ia32-libs to make Osmos work. (However, when I wanted to play Osmos yesterday, it suffered from the same "UI not updated" problem..) I've removed ia32-libs and all the dependencies that were automatically installed with it, but it didn't fix the steam problem.
My system setup has changed a lot recently, and I can't really tell when the problems have started. I've switched to Kubuntu 12.10 from Ubuntu 12.04 a few days ago. If I remember correctly, steam worked without problems at first even with Kubuntu. I've removed anything belonging to steam that I could find (the package, ~/.steam, ~/.local/share/Steam and some ~/.steam* files) and reinstalled, but it still fails.
Here's the console output from starting up steam, switching to the "Store" tab, then shutting down via the Steam menu:
My system info: