Additives (that often are synthetic) that cause adverse health effects if consumed regularly, like how yellow food dyes can cause hyperactivity in children and allergic reactions. That's one example.
Well, that's not a strictly proven link; the FDA, EU equivalent and the UK FSA dispute there is a known causal link. I think you're referring to a study from Southampton University, published in 2007 in the Lancet, which suggested such a link.
However, this study has a problem in that it studied a combination of dyes and sodium benzoate. The former could be easily omitted from food if found to be harmful, the latter not (it's a vital preservative, preventing the growth of microbes in things like soft drinks). Concern was also raised in that it relied upon subjective parental opinion in assessing 'symptoms'; this is often a clear cause of bias.
So you have to bear in mind these are very rarely clear cut things. It's extremely difficult to study them, and the aforementioned study has to be considered alongside numerous other double-blind randomized studies that
didn't find any link.
Yes, there are aspects of industry lobbying to deal with - the new 'traffic light' packaging employed in the UK is a classic example of this (in short, industry input resulted in a packaging standard for nutritional info that obfuscated rather than clarified how healthy the various fat, salt, etc levels in food were; recommended salt guidelines were also relaxed in response to lobbying, in spite of scientific evidence). The problem is there's also a set of fairly paranoid crusaders for the removal of additives, normally associated with the organic food movement, which feeds media disinformation.
Additionally, many additives -which are synthesized for commercial, mass manufacture and, yes, even safety reasons - are simply copies of chemical compounds taken from nature. The aforementioned sodium benzoate, for example, is found in cranberries, prunes, greengages, cinnamon, ripe cloves, and apples - the levels in organically grown prunes or cranberries can vastly exceed the safety limits set for this compound as an additive in drinks.
But we do actually need additives in order to produce the food at a level and price to feed our population(s); and whilst some are harmful, it's important to note
everything in certain quantities is harmful.
(NB: the thing about organic food is that it's not really about healthiness - there is definitively no difference in the safety and nutritional value of organic versus non-organic food - it's used more a status symbol
NB2: additives are also present in organic foods - currently 22 additives are licensed for this purpose in the UK)