An infant mattress (or other sleep surface) that is too soft can be dangerous to infants. A firm mattress might help prevent Sudden Infant Death Syndrome (SIDS). You can test a mattress's safety with two milk cartons and a stack of CDs. In addition to making sure a mattress is safe, you should take other means to assure your infant's safety when sleeping. A safe sleep environment is vital to a baby's well being.
While you might be okay if you know exactly what you’re looking for, some studies have linked the use of old crib mattresses with an increased risk of SIDS. concluded that there was a “…valid statistical associated between sudden infant death syndrome and the use of an infant mattress previously used by another child…” and I would therefore never recommend letting your baby sleep on a used crib mattress.