Some tests for freshness I found on the internet - can't be sure they're right but it's a place to start.

Baking powder: Mix 1 teaspoon with 1/3 cup of hot water. It it foams vigorously, then it still has rising power.

Baking Soda: Mix 1 1/2 teaspoons in a bowl with 1 teaspoon of vinegar. It it fizzles, then it will still help leaven a food made with flour when it is cooked.

Olive Oil: An unpleasant smell or taste indicates the oil is rancid or oxidized.

Shortening: Stored too long it will go rancid and develop a bad taste and odor.

Spices (ground): Smell a ground spice to check if aroma is potent.

Vinegar: Vinegar sold commercially is pasteurized. Therefore an unopened container should last indefinitely when stored in a cool and dark place. Once opened however, vinegar should last about 3 months if tightly sealed. Freshness test: Any sediment that develops can be strained out. Vinegar should be clear and look clean, not cloudy. If mold develops later, throw the vinegar away.