Condensed milk does go bad, or spoil. To prevent food borne illness, the best option is to use the milk before the best-by date on the can.
When properly stored, condensed milk can be used for quite awhile. After opening, condensed milk should be stored in an air-tight container in the refrigerator. In this way, opened condensed milk can be safely used for up to 3 weeks after opening. Unopened condensed milk should be stored in a cool, dry place, such as a pantry, and can be used safely for up to one year. If the milk turns yellow or is too thick to pour, it may be spoiled.