Haha! YES!

BRACES! THEY WORK!
The unit is now sitting comfortably on a desk, without falling apart. It can also handle full 360-degree rotation. I managed to get some ugly brace system going halfway down the legs of the tripod.
I also put rubber feet on the legs for 'added grip.' Before, the legs would slide outward and it would fall apart on the desk, but the friction on the carpet kept it together.
That was also before I got the braces to work, so I'm not sure how much they're needed now.
Oh, oh, and I also have the angle part of the legs (up at the connection between the legs and the turntable) using a triangle instead of the 120-degree bend pieces I was using earlier.
The weakest part of the unit is still the turntable, and the joints between the turntable and the legs. However, this is built up and made ugly so it's sturdy enough to survive.
Let's see if Lein can't get some better pics of it.
Edit: I should talk about the software. Because I, *cough cough*,
lost the light sensor somewhere...

...
Even if I found the light sensor, I doubt I could make it detect motion too well. The problem is that a light sensor is just that: It detects the light in a particular direction. If it's swivelling around a room, then it would see changes in light - and how would it tell between a change in light that signals a dresser, or a person moving?
Thinking about that, I 'could' set it up so that it records the light around the room and makes sort of a 'map.' Then it just compare light to the 'map' and can tell if something is out of place.
The problem with doing
that, however, is that the rotation of the unit can become mis-aligned with where it thinks it is in the map. I'd need a rotation sensor to check it, and I don't even have one of those.
The best I could do is have the turret fixed in position and tell whether there is motion that way, but now the problem becomes that the default mindstorms programming language is, well...
very thin, to put it mildly.
So, right now, the best that it can do is turn around in circles and start 'firing' when it pretends it sees something. (Random times)