Label reading is the most important thing you can do when you are shopping for food. Even the "all natural" foods can be tainted with additions such as wheat, milk, soy, nuts, etc. Fortunately, there are new regulations which require food manufacturers to list the ingredients which are allergy-triggers at the end of the ingredient list.
If you have a magnifying glass, and don't mind reading all the mile long names of who knows what in that box or bag of food, be my guest! It is much more time efficient to scan down to the allergy list, cross your fingers, and hope for a clear-to-buy!