One is that different types of food have different breakdown products, high protein foods usually give off ammonia and/or amines, low protein ones tend to be heavy in organic acids.

There is decay from stuff growing on it, breakdown of celluar structure, and chemical reactions such as oxidation. The third mostly ruins the taste and texture, the second makes the food unpleasant – slimy for example, the first can threaten health. The products from each will usually be rather different.

You could have several sensor layers, but checking for acids has the disadvantage that vinegar or pickled foods could trigger a warning. Matter of fact, many fermented and aged foods are “spoiled”, cheeses such as brie release both ammonia and acids, and consider S.E. Asia fish sauce.

Biological detectors might work better, tune them to detect DNA of the more common decay critters.