Is there any risk of illness from eating pasta sauce?

Yes, but it's a very small risk. Because of the way some pasta sauce ingredients are farmed, harvested, and processed, sauces may be contaminated with E. coli, salmonella, and Listeria. These ingredients include, but are not limited to, dairy products (cheese and milk), meat (beef, veal and sausage), seafood (shrimp and anchovies), tomatoes, onions, and  peppers. However, FDA mandates that all pasta sauces be pasteurized, either immediately before or after packaging the sauces in jars, pouches, cans or other containers. Heat pasteurization is a common method of killing food-borne bacteria.
 
Pasta sauce also may contain common food allergens, including dairy products, soy, and seafood.  Do not assume tomato-based products are free of dairy allergens. Some contain milk products to achieve a creamy or cheesy flavor. Check the label if you or someone you’re cooking for has food allergies. 
 
Once opened, pasta sauces are also subject to mold growth and  to spoilage (for example, deterioration of taste, smell, nutrients).    
 
Fortunately, proper storage, handling, and preparation of pasta sauce eliminate most risk of illness.
 
Source(s):
Barilla "Frequently Asked Questions"
Food Engineering Magazine "An Extended Romance: Minimally Processed Foods"