What Would Cause My Dog To Drool Constantly?

You may want to get his teeth checked out my your vet. Dental problems have many symptoms (food dropping,inflammation,low appetite),but drooling is definitely one of them.

Drooling can be a sign of oral irritation or nausea.  Oral irritation can be secondary to a taste reaction (ingesting something spicy or bad tasting), oral ulcers secondary to caustic substances, tooth root abscesses, and oral foreign bodies.  There are many things that can cause nausea.  I would have your dog examined by a veterinarian to determine the cause of the drooling and start appropriate treatment.
If this is a taste reaction you can try giving a small amount of milk or tuna juice to remove the poor taste in his mouth.