Profile photos on a desktop browser seem to be pretty low quality and have a lot of compression noise. See good examples below. It's noticable the most when there is a solid background color.
I wasn't sure what resolution I had originally uploaded, so I re-uploaded at 600x600 and it made no difference. Looks like the photo is scaled down to 128x128 anyway. I tried saving out that size and uploading, but still no difference.
I can't notice this on my iPhone since the image is so small and you cannot enlarge.