You can do generic tests like testing for toxicity, but that won't give you the full picture.
If you don't have a list of all the input raw materials, intermediates, by-products, impurities, surface materials that can leech into the final product, etc; you can't test for them.
That's true in the least helpful sense. We only know a subset of potential problems when it comes to food contamination and certainly don't test for all of even those. We naturally have no idea about the effects of yet undiscovered contaminants.