Yes molasses does eventually go bad.
When molasses expires and goes bad the molasses will begin to crystallize and when you see the molasses has crystallize then it means that molasses has gone bad and should be thrown out.
Molasses when kept sealed and never opened has a shelf life of around 10 years and after 10 years the molasses goes bad and crystallizes.
When you open the molasses then the molasses usually only lasts for up to 2 years before it goes bad and crystallizes.
It's best to use the opened jar of molasses within a year or two for the freshest molasses and the sealed jars of molasses are best used within 5 years but the molasses will last for up to 10 years and remain safe to eat.