Your site is likely re-sampling your file, perhaps because it is too large. Ask the Webmaster what size and quality to make the JPGs, and export to that. There may also be a browser issue.
If you provide some details re: exactly how your are exporting, which site you are using, how the JPG is used, etc., someone here may be able to provide additional guidance -- but this seems to be a Web question, as Aperture -- from what you say -- is working well for you.
Thank you for the reply.
I changed the Retina display optimization to the more space option and no longer have the problem. Typically I post to Flickr. I am new to mac and aperture but when exporting the pic I select export, version, and select fit within 1024x1024 and quality is 10-11. I then upload to Fickr. Hope this correct.
This is pure speculation since I don't have a RMBP, but perhaps the issue here Flickr's site doesn't yet generate retina sized thumbnails? Using the "More Space" option basically reduces the size of user interface elements so that the pixels are displayed at something more like a 1:1 ratio, which would at least appear to resolve the issue.