Fast, self-service store
We hate waiting in line at the cashier and stores don't like paying cashiers so some have self-service cashiers which are still hard to use. So here's an idea.
Provide shoppers who wish to self-serve a scanning wand, which is battery powered and attached by coiled cable to the shopping cart. In the shopping cart, have a number of shopping bags present and numbered. Paper bags which hold a square shape are better. Also have an open area or special bag.
As you pick up an item you scan it and put it in a bag. It would probably tell you which bag to put it in, though in some cases you could pick and tell it.
However, if the item is "unverifiable" then the scanner would indicate it should be put in the special bag.
An unverifiable item would be one whose weight can't be reliably measured. That's because the idea is to verify the main bags at check-out by weighing them. That weight should match the calculated weights for the items put in the bag, plus the weight of the bag of course. If the weight matches, the bag is just loaded back into your cart. If it doesn't, the items are scanned by the cashier as they normally are today.
Sometimes, even in a bag that matches the weight, a random scan of a few items in the bag would be done. Along with a basic visual check every time. This is to stop people from gaming it, by finding expensive items (notably pills) that happen to in combination weigh close to what some cheap items weigh.
Items of very small weight would go in the unverifiable bag, along with the most expensive items (just so that clerks know that they should never see them in the self-checked bags on visual inspection). Items of large weight would not be put with items of tiny weight in the same bag. Bags would also be balanced by weight, and a smart system would know to put cold items together, and not to mix cleansers and food.
Variable weight items, like meat, usually already have their weight encoded in the barcode as they are priced by weight.
There already are self-checkouts, and they do use a weight check, but it's one item at a time and they are a pain to use -- so much so that I have seen people reject them with just a couple of items. I am guessing scan as you shop will seem to add almost no time. Of course you will need buttons on the scanner to remove items, and even to move them to other bags when it won't hurt the measuring system.
Check-out will be with a cashier, but the cashier will simply place the bags on a scale, and if it beeps correct, put it back in your cart. They will do a quick visual scan (seeing the list of items and the order they were put in the bag on the screen) and if told to by the system, do a random item check. Sometimes they will even do a full re-scan of everything, but ideally this would be rare. Then they would hand check the specials bin, the way they check everything today. And then take your money. You should be through the cahsier in 1/2 to 1/3rd the time. A small number of cashiers would be open for those who wish to have everything personally rung up by the cashier.
Note as well that with this system you don't need to bar code the individual products! It's sufficient to have a bar code on the shelf tag, and to scan that, though of course people will get errors sometimes. The screen on the scanner would possibly show a picture of the item so you are sure you scanned the right shelf tag.
In the produce department, you would pick up vegetables, put them in a bag, and put them on the scale. It would show you the weight and price and also beam that to your scanner. Items priced by count would have to go in the specials bin unless they are all so close in weight that the scale can figure out the count based on the weight. I suspect this would work with most items in fact. (You would need to scan the shelf tag before heading to the counting-scale for these items.)
Of course it's also possible that regular customers could just get dispensation to just put the bags on the scale and walk out (auto-billed to their credit card) but frankly I am not that in favour of systems (like the discount cards) which generate giant databases of everything you buy.