I was lucky enough to stay at home with my kids for four years while my wife ran her own business, and during that time I got used to doing all the errands. Groceries, doctor appointments and preschool drop-offs were all mine. It worked well with our schedules. I had the flexibility to run around town during the week (the grocery store is a much more pleasant place on Tuesday mornings than weekends), and she could concentrate on her work. But when I went back to work full time this year, I had a hard time handing over that responsibility.
It's not that I didn't trust my wife to do these things; we just weren't used to having to think about it. Now we have to plan ahead.
Guys like things to be convenient, and you have to appeal to his sense of fairness when divvying up the errands. Ask him to make the trips that make sense because they're on his way home, close to his office, etc., instead of just saying "it's your turn." And always pitch an errand as a chance to get out of the house.
Who's in charge of the kids?