It feels like I'm repeating myself, but here goes anyway: Always read ingredients lists! As you've said, even the most innocuous products will contain questionable ingredients, especially if it's from a big company.
No matter what warning labels exist on the packaging, the ingredients list is always mentioned, as required by law. I almost never buy anything without having had a read through the ingredients, even if the product is labelled "vegan", since that doesn't preclude certain ingredients I avoid, such as hydrogenated fats, aspartame, white sugar, carrageenan, etc. I don't check labels on a bag of apples (other than the "organic" one), but most packaged products are suspect.
We'd all prefer to have all sorts of labels on our food, hey, I'm sure we'd all prefer to live in a veg*an world, but since that's not the case, the least we can do is watch out for ourselves. Reading ingredients list can develop into a fine skill, and you'll be able to skim read for potential non-veg*an ingredients in no time.