Forgetting about the Android part of this camera for the moment, overall photo quality from the Nikon Coolpix S800c is above average for a point-and-shoot with its features, suitable for prints up to 8x10 or slightly larger and Web use. You will get better photos (and videos, for that matter) from it than from a smartphone, barring top models like the Samsung Galaxy S3, HTC One X, Nokia 808 PureView (and probably the Lumia 920), or Apple iPhone 5. Even against those, it's better in low light.
Though its sensitivity settings run from ISO 125 to ISO 3200, the S800c is best used with plenty of light to keep sensitivity below ISO 400. Regardless of sensitivity, photos can appear somewhat soft and benefit from sharpening with photo-editing software. There's a Fixed Range Auto option that will limit you to ISO 125-400; I recommend using it in daylight when possible.
The two highest ISOs -- 1600 and 3200 -- should only be used in emergencies, mainly because the colors get very washed out and the noise reduction makes subjects appear smeary and flat, and actually, colors are so bad at ISO 3200 you probably shouldn't use it at all.
Colors produced by the S800c are bright and vivid up to ISO 400 and close to accurate, which you typically don't get with smartphones. Color quality tanks above ISO 800, becoming desaturated and muddy. Blown highlights were also an issue, but that is typical of point-and-shoot cameras.
The S800c can focus as close as 4 inches from a subject. This is a 100 percent crop of the inset image taken at ISO 125. Fine detail is good, but not great, and you can see noise and artifacts. Basically, don't expect to enlarge and heavily crop images and get great results, but they'll be fine at reduced sizes.
Zoom range is certainly one of the big reasons people still want a pocket camera. The S800c's goes from a wide 25mm (top) to 250mm (bottom). It has optical image stabilization, too, something not found in smartphones. (The Nokia Lumia 920 currently being the exception.)
Nikon corrects for distortion at both the wide and telephoto ends of the lens (top and bottom photos, respectively). The lens is fairly sharp in the center, but softens as you head out to the edges and in the corners. Also, though there is some purple and yellow fringing in high-contrast areas of photos, it's only really visible when photos are viewed at larger sizes on screen.
The S800c can capture three-shot bursts at 7.9 frames per second. However, focus and exposure are set at the first shot, so if your subject is moving, chances are good all three shots won't be in focus.
The camera also has 60fps and 120fps bursts; the former captures up to 25 images at a resolution of 1 megapixel, and the latter grabs up to 50 VGA-quality shots at a press of the shutter release. There's a substantial wait while the camera stores all those photos, but if you're trying to capture a specific moment in time, this is your best bet with this camera. Also, with all of these modes, the focus, exposure, and white balance are set with the first photo. If you have a fast-moving subject, like someone running, there's a good chance your subject won't be in focus for all of the photos.
Of course you have a whole ton of Android apps available to you for shooting and editing. This was taken with Urbian's Retro Camera and while you get all the things it offers, you do not get Nikon's controls over the camera. That means you don't get use of the zoom lens or control of other aspects like ISO or white balance, only what the app and Android allow.