FWIW, with FF 24, I see the xenopeek image, with 24 bit display (32bit display = 24 bits + 8 bits transparency, so they should look the same).
The bad image looks like a low-quality (high compression) jpg image. If the downloaded image looks bad in gimp/whatever, try converting it to png or bmp and see what that looks like. If it's also happening with Chromium, perhaps reinstall the jpg rendering libs....but I'm not sure which those are.
Are you using proprietary display drivers or nouveau?
Mint 17/Xfce/fluxbox & Mint 16/Xfce/fluxbox