Baking soda does expire, but that doesn't mean that it turns moldy or starts to smell. When baking soda expires, it loses its ability to work as a leavening agent when it's mixed with other food products.
While baking soda boxes do come stamped with an expiration date, this date is not 100 percent accurate once the box is actually opened. There is a test that can be done to test the potency of baking soda. Mixing a tablespoon of baking soda with a few tablespoons of vinegar tells someone whether the baking soda has expired. If the soda still bubbles quite a bit in the vinegar, it's still good.