Yes, shortening can go bad. You can tell because it will have a bad, rancid smell. In making a cake, I once used an opened container of shortening that I had stored in our pantry for at least a year. I had thought shortening lasted much longer on the shelf, but I was wrong. It smelled bad when I mixed it, bad in the oven, and bad as the cake cooled. I smelled the container and that was even worse. So you will know! Shortening that is still good should have almost no smell.
So how long can you keep shortening? Crisco has a helpful guide, which says that once opened, a can of shortening should be used within a year. The U.S. Department of Agriculture recommends even less time — three months. So use your judgment (and your nose). It’s helpful to write the date that you opened it on the lid with a permanent marker.
Keep shortening in a cool, dry place once opened. For easier spreading, don’t refrigerate it.
An unopened can keeps for two years from the manufacturing date, according to Crisco.