There are various possible reasons for what you are experiencing, but here are the some of the most common reasons for each:
1) Loss of sharpness when viewed outside of PS: The viewer likely has its "fill screen" or "fill window" option turned on, and your image was either around the same size as your screen/window or, most likely, smaller, so the viewer had to up-Rez your image. Such resampling always introduces a softness in the image. The solution to this is to (a) either use an image viewer that doesn't do this, and/or (b) always save your image at as large a size as possible so that the viewer is always forced to down-Rez the image for display as this preserves apparent sharpness better than up-Rezzing.
The second common reason people complain about an apparent loss of sharpness is that they are actually not seeing a loss of sharpness, but a loss of contrast (which many people interpret as a loss of sharpness).
2) Color, saturation, tonality shifts when viewed outside of PS: Unfortunately, many image viewers *still* aren't properly color managed. They interpret all images as sRGB, even if the image is properly tagged as being in another color space (eg, Adobe RGB, ProPhoto RGB, etc.). The most likely reason you saw such shifts is that you failed to convert your image to sRGB before saving it as a JPG. While doing so may reduce the gamut of your image, this is a small price to pay to ensure that you image will display properly on the widest variety of software and hardware.
HTH,
Tom M