Overall, the S4500's photo quality is good as long as you're willing to work within its limitations and you're not expecting dSLR quality just because it kind of looks like one. But, if you're the type to never leave auto or use a tripod, you might not be 100 percent happy with its photos.
Basically, like most lower-end to midrange compacts, the S4500 can take some nice photos below ISO 200 that can be used at reasonably large sizes. The more you have to go above ISO 200, however -- whether for shooting indoors, using the zoom lens, or both -- the less satisfied you might be with the results.
Without enough light, the camera will boost the ISO to keep shutter speeds fast enough to freeze movement (and this camera's lens needs a lot of light). However, increasing the ISO also increases noise and noise reduction that in turn softens details. Once the S4500 hits ISO 800, though, it will start to use slower shutter speeds to get the correct exposure. Depending on how slow it gets, if you're not on a tripod and your subject isn't still, you'll end up with soft, blurry photos. (You can see examples of this toward the end of this slideshow.)
This is common with this class of camera, not just the S4500. What is specific to the S4500 is the photo quality at ISO 800, which is OK for Web use at small sizes if you don't mind softness.
Something goes horribly wrong at ISO 1600 with color and subjects really are just too soft, so I would avoid using this or the higher ISO settings available at reduced resolutions. On the upside, Fujifilm doesn't use this setting when shooting in Auto; it will drop the shutter speed instead.