I'm not entirely clear what you mean by "quality", if you mean the quality setting in the JPG compression algorithm then you may be able to extract it from the EXIF tags of the image (relies on the capture device putting them in and no-one else overwriting them) for your library see here:
http://www.aurigma.com/Support/DocViewer/30/JPEGFileFormat.htm.aspx
If you mean any other sort of "quality" then you need to come up with a better definition of quality. For example, over-exposure may be a problem in which case hunting for saturated pixels would help determine that specific sort of quality. Or more generally you could look at statistics (mean, standard deviation) of the image histogram in the 3 colour channels. The image may be out of focus, in which case you could look for a cutoff in the spatial frequencies of the image Fourier transform. If you're worried about speckle noise then you could try applying a median filter to the image and comparing back to the original image (more speckle noise would give a larger change) - I'm guessing a bit here.
If by "quality" you mean aesthetic properties of composition etc then - good luck!