The problem with taking The Caterpillar to any store is that she's into the Grabby Sam stage of development, where she'll risk life and limb to get whatever catches her eye. While shopping, this means that even when she's sitting happily in the basket of the shopping cart, as we pass by some desired item she will lean out to grab what she wants without regard to the fact that she'll throw off her center of gravity and end up backasswards on the floor if you're not there to catch her. Or when she decides she's done with the cart, without notice she'll just stand up and heave her weight toward you over the bar, fully expecting you to catch her before she lands like a splattered orange on the concrete floor.

Leaving her out of the cart isn't an appropriate option either. In that case she'll clear every shelf below twenty four inches of it's stacked items like an excited Great Dane puppy sweeping everything off the coffee table when he wags his tail.
The other day I discovered the secret to going to the store with The Caterpillar and I'm going to share it with you because I'm altruistic like that. Here goes:

Let her pick up something right away and latch onto it - encourage her to get two, one for each hand. Then she can walk all around the store on her own power as she wishes, you don't have to be constantly on alert for when she decides to stand up in the cart and hoist herself out, and because her hands are full she won't try to pick anything else up. You don't have to bend over every thirty seconds to put back something she's knocked off the shelves.
Then just before you go check out, take the two things away from her and put them back. There will be some protest, but by this time she's begun to tire of her items anyway and it generally doesn't last long.

The other morning we went to CVS and she picked up two toilet plungers. If you want to get a bunch of raised eyebrow looks from strangers, let your baby walk around the CVS with toilet plungers in both hands.

Hey, it works.