I had this problem myself, searched endlessly for an answer and found none. Until I found someone who did not have this problem, I asked them to share their wallpaper with me and I tried it, sure enough, their wallpaper did not have any on screen artifacts and the resulting compressed wallpaper, was not a shrunken down jpg. In fact, the file size of the "compressed" jpg was larger than the original.
So I decided to look around into the settings on the jpg, nothing unusual that I could see, the image was 1900x1200 at 72.009dpi and 8bit. I decided to scale down my own personal wallpapers to the 1900x1200 size, changed the dpi and bitrate to match the other jpg. After saving my new image, I right clicked on it and chose set to desktop, the resulting image has no artifacts and is no longer compressed. This works for every wallpaper I have.
If you try this, I think you need to make sure you change the image dimensions to match that of what your screen resolution is exactly. Also making sure the dpi is set to 72.009 and 8bit. Try it out, see if this helps anyone. I will be posting this message on all the forums and blogs I see discussing this.