Corn syrup from the grocery store has additives you may not want in your beer - vanilla for one. It's not pure dextrose either. From Karo's web site:
What is corn syrup?
Corn syrup is a mildly sweet, concentrated solution of dextrose and other sugars derived from corn starch. It is naturally sweet. Corn syrup contains between 15% to 20% dextrose (glucose) and a mixture of various other types of sugar.
What is the difference between Karo light and dark corn syrup?
Karo light corn syrup is a mixture of corn syrup and high fructose corn syrup (to provide increased sweetness) and is flavored with salt and pure vanilla. It is clear and colorless, with a moderately sweet flavor.
Karo dark corn syrup is a mixture of corn syrup and a small amount of refiners' syrup (a cane sugar product with a molasses-like flavor). Caramel flavor, sodium benzoate (a preservative), salt, and caramel color are added. Dark corn syrup has a rich brown color and distinctive flavor.