You can mulch your paths with old cardboard, but definitely check to see if it is printed with ink. If it is, you want to be sure it has only black ink. Most black inks are made from soybean oil. Only use the material for paths. Paper and cardboard printed with colored ink is another matter, as this ink may contain some toxic heavy metals. Avoid using cardboard or paper for mulch if it contains colored ink. Of course, if your cardboard is more than merely dirty and has absorbed oil or other chemicals, it should probably not be distributed onto the ground.

I think it's always best to reuse and recycle materials as close to home as possible. Using cardboard for mulch, is certainly better then recycling it or burning it.