EPS is a flat file format. This means anything with uses blending modes, some appearance settings, or transparency within Illustrator will be flattened upon saving to EPS.
Without seeing the actual final result, I would guess that flattening occured when you saved the file resulting in the "artifacts" you are seeing. It's always a good idea to utilize the Flattener Preview Panel within Illustrator before saving as an eps or conversely, close the file after saving to eps and then reopen it to see what has taken place regarding flattening.
Files often require special care when saving to EPS to ensure appearance is as desired.