Posting ,jpg image on Mac/Facebook

The main possibilities:

• Too few pixels. Facebook probably tells you the optimum number of horizontal and vertical pixels for its various sized images. If you are designing in photopaint, set that as your paper size and check when you export to jpg that the export dialogue shows the same sizes.
• Too much compression. Does facebook support PNG? That's easiest, because there are no options. But if only jpg is allowed, try saving at 30%, 50% and 80% quality level and compare the results.
• Wrong colour mode -- for any web site, make sure you are exporting to RGB not CMYK.