Is there any risk of illness from eating a steak dinner?

Yes, particularly if it isn't thoroughly cooked. The major concerns are the pathogens salmonella, campylobacter, and E.coli. Although meat processors must have food-safety protocols in place to ensure all packaged product is pathogen-free, disease outbreaks from these pathogens can--and sometimes do--occur.  The good news is that whole-muscle cuts such as steaks and roasts are sterile on the inside. Additionally, cooking the meats destroys any pathogenic bacteria on the outside of these cuts.
 
Spoilage bacteria may also grow on beef  if it is not stored at a temperature of 40°F or less or if it is stored at an accepted temperature for a prolonged period of time. (Spoilage bacteria may ruin the taste, smell, and/or looks of food but generally don't cause illness.)
 
Additionally, whole-muscle beef is subject to mold growth once it has surpassed its shelf life.
 
 
Fortunately, proper storage, handling, and preparation of whole-muscle meats eliminate most risk of illness.
 
Source(s):
USDA Fact Sheet "Food Illness and Disease"
American Meat Institute Fact Sheet "E coli O157:H7"
USDA Fact Sheet "Beef...From Farm to Table"