I hate to come in between you and his dad here, but while it's an excellent idea to teach a young child to be clean and act responsibly, giving him a job to do....I don't think this is advisable in this case. If totally supervised by an adult -throughout the picking-up, and hand washing afterwards(!) then ....maybe. Otherwise, a four year old can easily make a mistake, do something unhygienic, put his fingers into his mouth...etc.
It's not worth the risk. That's my opinion. There are some dangerous diseases easily caught, such as Toxocariasis.
Toxocariasis is an infection of the round worm Toxocara canis5. It is a disease that is spread via unwashed vegetables and dog feces. Young children in particular are at risk due to their weaker immune systems and because they are more likely to expose themselves by ingesting the eggs.
I agree, have your son take out the trash or something apropriate for his age, picking up poop isn't for a four year old. Its a job the adults hate, and their dumping it on your son.