Charlie Howard (Steve's Digicam, Panasonic forum, 15 January 2004)...
For me, the two problems with FZ10 indoor photos were White Balance and an early mis-impression that I could take good pictures without the flash.
But, without the flash, the yellowness of indoor lighting gave all of the pictures an orange cast. That's normal with many digicams, and the FZ10 provides a nice built-in solution: the right-most choice on the WB menu lets you aim at a white surface (a wall or ceiling, for example) and click the shutter so the camera can adjust WB to the lighting. Once you do that, colors will become normal again.
Without the flash, slower shutter speeds were needed, and I couldn't hold the camera steady for that length of time. The people also moved, of course.
So, it turns out that there are some big advantages to using the flash: the colors will be correct with Auto WB, and the brief duration of the flash means you can use a very fast shutter, which reduces blur due to subject or camera movement. OIS probably gives you the equivalent of 2 extra f-stops, so instead of having to shoot at 1/100 sec, you could shoot at 1/25th; but if the shutter has to be open for 1/4 second, you still may get some blur (depends on how steady your hands are). And, of course, your subjects may be moving.
Finally, as Panasonic Bob explained, an external flash is very helpful. Within that big zoom lens lies a subtle snare: with a normal camera, if you want a close-up, you have to stand close to your subject (6-8 feet, right?), but with the FZ10, you can stand across the room, 20 feet away, and use a 4x zoooooom for your close-up, making it seem as though you're only 5 feet away. Unfortunately, if you're 20 feet away, with a flash that's effective out to 8 feet, you'll get an underexposed photo. The solution, as Bob said, is to use an external flash (or to get closer).
{Picture below `Tree Reflections' by Charlie Howard taken with FZ10, but without a flash!}