There are multiple layers of response to such "problems". (if society actually considers them problems) In this example, the high numbered items are less likely to happen than the lower numbered items.
Most people like food labeling requirements. Truth in advertising. That's what we're used to, so that wouldn't change. The only thing that changes is the specific requirements and enforcement mechanism. The grocery store would mostly likely have contracts with their distributors that enforce specific requirements, and they would advertise those publicly to get more business - creating an implicit contract with the customer. In some ways food regulation might be worse under Ancap, but it would be exponentially better in other ways. With such requirements in place, customers can bring a claim if they're found to be violating it. First you'd complain to the store which would complain to the distributor. Failing that you'd bring a suit against the store AND the distributor to a court specializing in food safety or consumer protection. Ideally most of this would be handled between your and the store's insurance companies.
There would most likely also be private law in the city or neighborhood in which the store resides (most businesses/grocery stores lease their property) that takes effect in the absence of another contract between the store and customer. In this case you'd follow whatever the local law says, which might not be that much different than city health ordinances today but with added sanctions against the business and/or personal restitution.
Sometimes you'd find that cheap stores would openly put filler in cheap food for poor people who have to shop there because they don't have a choice. Instead of paying taxes, people would give money to charities and activist groups that engage in media pressure campaigns to force companies to regulate their products. This isn't much different than now, but those groups would be stronger and have more funding. There are many levers of power beyond legislation.
In any of the above instances, lacking an explicit or implied contract with a seller, you could file a complaint in a general arbitration court by arguing that putting harmful ingredients is violation of the NAP. Especially if you haven't disclosed those ingredients. The above groups would help poor people do this. The only thing preventing it would be if the company was strong enough to "own" all the courts who might be powerful enough to enforce rulings against them, and threaten private investigators/the media to stop investigating. In that case you have a defacto State again, so we're not talking about Ancap any longer.
If all else fails and Señor Greedy Moneybags ends up killing the wrong person with his fake food schemes, somebody would take care of it. Maybe he'd have a boating accident or extreme guilt would drive him to jump off a building. Ancap is about non-aggression but you're not going to change human nature. If people know he was a bad guy poisoning people, nobody would bother hunting down and prosecuting whoever arranged his mysterious disappearance. The only reason it doesn't happen now is because of "The Law". "The Law" doesn't just protect the innocent but it often protects the guilty from getting the justice they deserve. (but again I want to stress that there are a lot of stopgaps before it would ever get to this point)
I probably missed a ton of options. With the State, there may be faster or stronger responses against improper behavior, but there is still a limited set of possible responses. Without a State, the sky is the limit.
Yes it is thought to mainly revolve around liability for (not) following explicit and implied contracts or for endangering others. Pretty much like tort law today but with parallel court systems, where the contract decides where cases will be heard, like in an arbitration clause.
And I totally forgot to directly answer the meme's "before people notice". Organizations like the USDA or accredited organic certifiers like NSF would basically be insurance companies and their investigation services. Respectable suppliers wouldn't operate without certification. So they would have regular inspections like they do today.