I have a 50mm prime lens, chosen due to great reviews. I bought mine second-hand from a very reputable store. Unfortunately, the 'sweet spot' (middle part of the image) is slightly fogged in my images. I think this comes from marks in the coating on the back glass of the lens. Cleaning with lens cleaning fluid has not altered the marks. Is there something else I can do?
Yep, I'd recommend returning it since if mild cleaning doesn't affect it, the coatings are likely scratched, and more vigorous rubbing will only make things worse (though I'd recommend trying a lens pen if you have one handy). In my experience, defects on the rear element are much more problematic than those on the front element, but that said, if it was a really good deal and you're set on keeping it, test it under some challenging lighting conditions and see how it fares in terms of sharpness and flare, maybe it'll be fine. High contrast areas are the first place I'd look for problems.