I have two images (PNG files). One of them is in multiply mode. When that file is in multiply mode the image is not as clean. The contour of the file is like little squares. That'a on a white background.
Is there a lot of compression on the image? The artifacts could be due to quantization (aka "jaggies") around the edges. They may be not very visible to the naked eye in "normal" mode, but using the multiply setting might be bringing them out. Do you have access to an uncompressed version of the file you could test?