I've played with underwater photography using a Canon S300 for a little while now. It's been a lot of fun to take the camera on dives, and I've even been lucky enough to get a nice shot every once and a while. One problem with using a point and shoot under water (or any camera for that matter) is that certain colors start to fade at depth because their corresponding wavelengths of light start to disappear. The reds disappear first, followed by yellow, and so on (there's a nice table here). Note the blue tint on the photo above. If I recall correctly, it was taken at a depth of about 40 feet.
To compensate for this, you can use a strobe (flash) to give you the light that you need. They have a limited range though, and have a nasty habit of lighting up particles in the water, creating a cloudy shot. You can limit those reflections, also known as backscatter, with a detached strobe that shines light at your subject an alternate angle, but those are rarely available for point and shoot cameras and are often prohibitively expensive. Believe me, I'd love to put my dSLR in a nice IKELITE housing, but I just don't have the bankroll for that.
You can also try a few post processing methods, one of which is well described at WetPixel.com. Divester.com has another.
Apparently, Alex Mustard has created some underwater filters which are reported to solve this problem when snapping pictures between 10 and 40 feet. Originally only available for dSLR cameras, Alex is now giving the point and shoots some love. Here's what Divester has to say:
I'm sure you know about Alex Mustard's Magic Filters, gel filters that help divers produce beautiful underwater images. For those of you who don't know, the reviews of Magic Filters have been glowing. The only problem with the filters has been that they're only for use with dSLR cameras. Until now.Does anyone have experience with these filters? Are they any good? I think that I'll give them a try. If/when I do, I'll post a photo or two here.