I have worked with a lot of children with autism and so I am going to give you some advice with what I know about those kids who throw tantrums about anything they don't want to do.
I AM IN NO WAY SAYING YOUR CHILD HAS AUTISM OR ANY DEVELOPMENTAL PROBLEM!!!! I'm just passing on advice based on what I know.
I think what he is doing is communicating with you that he doesn't understand or like what is going on. Most kids at this age rely on routines to get through their days and to understand the world. When you do errands, he doesn't know what to expect next and tantrums to say 'I don't understand and I don't like it'.
What to do: Have an age-appropriate conversation about what is going to happen that day. It may be helpful to cut out pictures (or take them with a camera and print them out) about what is going to happen (i.e., the grocery store, someone's house, the mall, your house...). You can glue them onto 3X5 cards and then give them to him to hold.
When you leave the store, give him a picture of your car or your next destination and tell him that this is where we are going next. Also, give him the choice of being held, holding your hand, riding in the cart... and let him pick what he wants to do. Give lots of verbal praise or a reward when you eventually get to the car without a tantrum. If you don't make it, turn around and go back. Say, "You didn't hold mommy's hand/go without kicking/go without yelling... and now mommy gets to pick how we go." Some stores will help you out with your purchases and this may be most helpful until he understands.
If this makes no sense at all please e-mail me at ____@____.com you hate this advice just ignore it.
I hope you find a soulution.
R.