Poor quality refers to the lifestyle descriptions on page 158 of the D&D 5e Player's Handbook. The food isn't spoiled or poisonous, so the food in the storeroom isn't dangerous, just of low quality.
A poor lifestyle means going without the comforts available in a stable community. Simple food and lodgings, threadbare clothing, and unpredictable conditions result in a sufficient, though probably unpleasant, experience.
The squalid and wretched lifestyle descriptions both refer to disease, so it might be reasonable to introduce disease mechanics if the food was described as of squalid or wretched quality instead of poor.
The full list of lifestyle quality levels, in ascending order of is: wretched, squalid, poor, modest, comfortable, wealthy and aristocratic. Any time you see "[thing] quality" for one of those, it likely refers to these lifestyle levels, and the full descriptions will give an idea of what exactly that means.