I notice it on your characters hair also - now when you say background, do you mean - background fixed image - or do you mean you used a 3D prop of a wall and used it as a background.
If you used the main fixed background for the image - not sure what that is ...
but if you used a prop - try using the "Alpha Threshold" check box, not sure if it will fix this problem to be honest - but usually when I have issues with images on props - this button often helps - especially with edges.
Another thing that comes to mind, based on the white in your characters hair - is the lighting - the way it's turning white is a reflection thing which you might be able to address with lighting angles in your render -
I'd also try playing around with the anti aliasing - another guess on that would be that with so many layers - some artifacts that weren't noticeable in the first image on your layer was getting progressively worse with each anti-aliasing treatment.
Kind of like with an mp3 - let's say you took the same approach of layers ...but with sound ....by the time you get to your final picture ....the 1st layer would have endured 10 generation losses from the constant reprocessing of adding each new layer and re-rerending.
Not sure if any of these are the answers - just giving some clues for a starting point as to what could possibly cause this.
Cheers and good luck!
☯🐉
"To define Tao is to defile it" - Lao Tzu