Corn is off the Paleo menu, because it is a grain. It is high in carbohydrates, low in fat, and the fat it does contain is mostly polyunsaturated fats (PUFAs).
Paleo and PUFAs
Those of us living a Paleo lifestyle try to limit our intake of PUFAs because they tend to be highly inflammatory. The invention of industrialized oils (such as corn) have introduced a record high level of PUFAs into our diets.
Omega-3 vs. Omega-6
Corn oil is especially high in omega-6 fatty acids, a type of PUFA that is highly inflammatory. Omega-3 PUFAs are anti-inflammatory and we should be eating at least as much omega-3 as omega-6, if not more. Thanks to the cheap, hydrogenated oils now available (and conventional wisdom’s conviction that butter is unhealthy), most Americans are consuming far more omega-6s than omega-3s.
Mark Sisson included corn oil is his guide to oils.