I took it into the Apple Store and they decided it was the hard drive. [They also thought it might have been my fault for installing a piece of software that wasn't compatible with that version of OS X, but we won't go into that.] They replaced the hard drive. Two weeks later, it started happening again.
I took it back, and they decided it was the graphics card, so they replaced the entire motherboard. This took several days, during which I had no computer, which may explain my later behavior...
After that, the machine worked, except for one problem; every now and again the screen would flicker - or have a black flash - that was about as quick as your eye blinking. It was enough to be noticeable, but not enough to really drive you crazy.
In fact, for a long while, I almost convinced myself it was just something they all did; I also thought at one point that it might be connected to the Flash player, but I couldn't prove that either. Only when I used another MacBook Pro for a period of time did I really realize that my computer was misbehaving.
Artist recreation of the issue
But by then it was out of warranty, and I wasn't sure I wanted to take it back and go through diagnosis and lack of computer time. I could live with it.
I also thought it might be a problem with the cable from the motherboard to the screen, perhaps it was crimped I thought, but the problem never got worse. So I just lived with it.
When out of the blue, Apple released a firmware update:
MacBook Pro EFI Firmware Update 2.8
The MacBook Pro firmware update is recommended for 15-inch, late 2008 models. The fix resolves a graphics issue that may cause the internal display to flicker. The file is a 1.79MB download and requires OS X 10.5.8, OS X 10.6.8 or OS X 10.7.3.
When I read the details, my first thought was: "Hey! That's me!" but then I thought "Surely, not!" because a) what are the chances that's the problem I've had for three years? and b) surely, they can't have just decided to fix it now?!
But I installed the update last night, and after several hours of usage I can report that - so far - it does seem to have fixed my problem! And it was flashing regularly enough that even an hour of no-flashing is a tremendous improvement!
So thank you Apple! Yes, the fix is about three years later than I would have liked it, but perhaps, like me, everyone who had the problem had just sat back and accepted it and never told you.
I guess I can't complain, if I hadn't complained...