Parental geniuses, I need help with my monkey of a 16 month old?

At 16mo, he's still a little dude. As someone already mentioned, distraction is going to be your best bet. Involve him in the shopping. Let him hold non-damageable items. Ask him which tomato/apple/potato he thinks you should choose. Talk to him about what you're doing, preferably in a silly voice. "Okay, here we go down the pasta aisle. Weeee neeeeed sommmmee SPAGHETTI! But Alden doesn't like spaghetti, does he? No way. That's one of his least favorite foods... right up there with cookies..." Just make it fun and engaging for him. I remember the grocery store as a little one -- it sucked. So much to see and touch, but I wasn't allowed to! Pure torture. Avoiding that sort of thing by letting him be part of the process is what generally works.

Pair that with gentle reminders that Mummy needs him to sit still. It might help if he doesn't have to sit in the little front seater the entire time. Can you carry him on your hip for five minutes? Let him toddle next to you for five minutes? Throw him in the basket with the foodstuff for five minutes? Then back to the seater. Repeat.

I have one of those and she's 4 now but thank god she still can be strapped in the cart. Wiggling ain't that bad my son use to pull down anything he could reach at the store so his sister being a wiggle monster I can handle. So my only idea for you is just get a sitter if you. Just remember it could be worse. He could be twins doing the same thing or one of those kids that scream I want no now now. So count yourself luck and hope he grows out of it. Good luck.

I made the mistake of taking my daughter out of the cart and letting her help me "push" the shopping cart. I mean, it isn't that big of a deal, but now she's 2 and thinks she can just get in and out of the cart and that she can walk around the store at will. It gets difficult sometimes. I don't recommend that, but perhaps you can put him in the basket part and as you get things hand them to him (unless they're breakable) and say "Can you put this in the cart for me?"

Distraction: Snacks, books, toys. Is there anything that holds his attention long enough for you to shop? Is able to walk, holding your hand? My 17 month old is the same. The only thing that works for me is holding him, whilst pointing out the products I'm buying.