If you want to train your dog not to eat that icky stuff, you might try a week or two of going out into the yard first before he does, and sprinkling the poo with hot cayenne pepper powder (or something else he hates). We have heard some people have had success with this method. Be careful--you don't want the hot pepper powder to be dusty and airborne and hurt your dog's eyes or nose! If your area is very dry, hot sauce might work better. Making that poo too hot to eat might train your dog to look elsewhere for snacks. Your vet or an expert in canines might have other suggestions.
Waiting for a doggie feast?
Birds are mostly insensitive to capsaicin, which is the "hot" element of the hot pepper, so it shouldn't affect your birds' grazing at all, even if you purposely spread it onto their pasture. In fact, many people use a hot pepper preparation in their wild bird feeders to keep squirrels from making off with all that seed!