I don't know how robust the study is, but according to The Guardian, young children fed a diet high in processed foods have lower IQs, and those effects persist even if they begin eating more healthfully later. (Via Jezebel.)
But, the thing is, we've spent the past few decades altering the food chain and our diets completely. Teasing out the individual effects that has is the very difficult work of science, and questions about broad, systemic effects are even more difficult for scientists to deal with than the norm. At the same time that we've changed how we eat, and increased the elements we know to be bad for us, like salt and sugar, we've seen a rise in the number of problems children have. Obviously, correlation doesn't equal causation in every case. But I don't see many arguments against eating well and eating better. The plethora of poor food options hasn't done anything to end hunger, which was what an abundance of cheap food was supposed to do.
