More recent observations with my camera:

I realized part of the source for my unhappiness with the focus system. I went and read the manual again, closely, and I now understand what I was doing wrong. As a reminder, the camera has five "focus zones", one center, one left, one right, one top, and one bottom.

There are two main autofocusing modes (with two variants of the latter mode). The "simple" mode, which you get when you select any of the "VariProgram" (read: idiot) modes, is that the camera will focus on whatever it sees to be closest in any of the five sensors. If you're a point-and-shoot shooter, or if you're shooting over your head and can't actually put the focusing zones on anything in particular, then this mode is the right one to use.

If you have the camera in "P" (program) or one of the other modes that give you more control (which you need to do if you want, for example, to use the SB-800 flash in commander mode), you have a choice of using a specific one of the five sensors ("single sensor") or a dynamic variant where the camera may somehow intuit that the subject that you initially picked up in the center sensor moved to the left, so the camera will continue tracking your subject on the left sensor. The dynamic mode is only likely to be useful for certain sorts of sport shooting. (Of course, you can also tell the camera that you still want the "closest subject" focusing mode.)

Anyway, when you're in the single sensor mode, you can manually choose which sensor is used. And, by default, this is selected using the arrow buttons on the back of the camera. I'd been bumping these buttons all the time and my chosen sensor had been moving around willy nilly. Unsurprisingly, I came out with some improperly focused pictures. Reading the manual closely, I now understand why there's a "lock" switch on the back of the camera. If you move it to "L", then your chosen sensor stays put, even if you accidentally press the arrow buttons. Proper use of the camera (which the manual was not terribly clear on) is to leave this set to "L" until such a time as you want to move your focus sensor selection. Only then would you switch off the lock, move the sensor, then turn the lock back on.

Score one bonus point for the Nikon ergonomics people for realizing they needed the lock switch. Score one penalty point for the people who wrote the instruction manual for not making this abundantly clear beforehand.

My next adventure: a close reading of the manual for my SB-800 flash.