I note that when doing a simulation in the the cloth room, the camera flys around in seemingly unpredictable and random ways.  At other times, it hardly moves at all.   It is usually not what I want - in fact, I usually wish it would stay still so I can watch a particular area of interest. 

My question:  can I control this?  Can I program it in advance?  Or is it at the mercy of some random operation in the program?  I find no mention of this fly-about in the manual.

Thanks for any clues

I have only used the cloth room a little, but if you move the camera around to inspect everything after the simulation is over with the last frame selected, the camera will have moved for the end frame. If you redo the simulation the camera will move to match its position at the end frame as the simulation goes on.  If you keep doing simulations and move the camera around, I have found it can move in some pretty funky ways. It sounds like maybe you are accidentally animating the camera to move. If that's the case just use one camera view to do work with, and use another one to remain stationary. I don't know if that is what is happening with you though, its just the first thing that comes to mind. Maybe someone with more experience with the cloth room could give a better explanation.

each camera has a setting in it's "properties" tab for animating. Just check the box or leave it unchecked. I usually turn camera animation OFF, since I make mostly static images.

Move a camera in a frame and it creates a keyframe. then it tries to animate to follow.

Press the "key" icon in the camera controls - it will turn off the animation for the current camera

Thanks very much to all of you for the help, especially to wimvdb for the easiest solution - the key icon.

When I first read about that, I dismissed it (and promptly forgot it) as unimportant, thinking I wouldn't be getting into animation.  Surprise - the cloth room uses animation.