Interesting, looks like laws differ in subtle ways for these kind of agreements. For reference in the Netherlands any offer you make is legally binding, though the deal has to make at least some sense to both parties (as well as satisfy a few other conditions).

A price of 1/5 ct would probably be considered too low to be sensible and would not be considered binding.

American Law is almost universally the opposite - HOWEVER it doesn't completely unlimit it - you'll see signs at grocery stores that say something like "in the event of a price error, the store must give you the item at the listed price refund the difference"

For example, Wisconsin:

98.08 Price refunds; price information. (1) A person who uses an electronic scanner to record the price of a commodity or thing and who sells the commodity or thing at a price higher than the posted or advertised price of that commodity or thing at least shall refund to a person who purchases the commodity or thing the difference between the posted or advertised price of the commodity or thing and the price charged at the time of sale.(2) A person who sells a commodity or thing and who uses an electronic scanner to record the price of that commodity or thing shall display, in a conspicuous manner, a sign stating the requirements of sub. (1).

https://glitchndealz.com/glitch-laws-by-state-pricing-error-...

How far would they have to go before they ran afoul of some sort of false advertising claim?

Presumably any legal system would treat the intent as the primary relevancy. In this case it is abundantly clear what the intent was (note that even the person complaining gives an explanation for what the store intended and thus is clearly not at all confused about the intent).

That sounds impossible to deal with. So you pick your groceries based on price presumably and then when you get to the register they can be something totally different? So as they are getting rung up you would have to say "no thanks for that one, please put it back" on every price you are not in agreement on?

Technically, yes, but practically obviously not because people who run shops aren't completely stupid.

Considering the recent news that online groceries can change prices (even dramatically) after you've ordered them, so supermarkets apply prices on the day of delivery, and you're on the hook for any difference... this doesn't surprise me one bit.