I put mine in shopping cart (Dahon Speed TR) all the time. Costco shopping cart... plenty of room (oversized shopping cart). Von's, Ralph's, etc (standard size) - just fine. Target, K-mart, Walmart (standard to slightly smaller) - just fine. Trader Joe's (smaller size) - I can put the bike in but... it's rather awkward as well as no space to put anything after.
I've yet to be refused of entry once I fold it up and put it in shopping cart at stores. I would think something with 16" wheel can probably accomodate even the smaller shopping cart fine... (or roll along...)
I did test ride folding bicycle concept for about month to two using really cheap (free to me... used to be $70 no name imported folding bike that was slow as snail with very awkward fold) to see if it's doable. Once I found it is possible, test rode few around and stuck with Dahon for it's value vs. quality of ride.
Very nice bike. I do 30 miles on it daily during weekdays.
I did save enough for spanking new Bike friday in the mean time but hasn't pulled trigger as I found I am not folding it as much as I thought for one... and the ride is more than adequate is another. Someday...