What exactly does "All Items Not On Sale" mean?
Solution 1:
I think the answers so far given are concentrating on "on sale", but I interpret the question to be about the scope of "all" and "not".
I first noticed, and was troubled by, the usage "all ... are not ... " to mean "not all ... are ... " about fifty years ago, when I was quite small. Nonetheless, this construction is widely used in English, with this meaning. Furthermore, it is not treated as ambiguous, because to express the "logical" meaning, we would use a different construction with "none" or "no": "No items are on sale".
An old example is the proverb "All that glisters is not gold".
(I agree with you about the unreliability of The mother tongue: he's a journalist, not a linguist, and it shows. I have recently read another book to which I have the same complaint: Planet Word, by J.P.Davidson)
Solution 2:
I've never seen that. What you do sometimes see is something like ITEMS NOT IN SALE. A sale, as you probably know, is a store promotion in which some goods are sold at reduced prices. Those that are not being offered at a discount are thus indicated. Bill Bryson, entertaining writer though he is, may, deliberately or unintentionally, have been misreporting.
Solution 3:
As others have noted, the ambiguity really has nothing to do with the word "sale", but with the words "all" and "not". If I said, "All of our employees are not accountants", does that mean that none of our employees are accountants, or that some of our employees are not accountants? Etc. That's why I'd generally say "none are" or "only some are" or some other alternative wording rather than "all are not".
I'm curious about the comment that this sort of thing might be a problem for a foreigner. I don't know any languages besides English (and a little stumbling Latin), but don't other languages have similar ambiguities? I'd be surprised if this was a problem unique to English.
Solution 4:
I think there's a BritE vs. AmerE issue here too.
In British English, "On sale" is the same as "For sale", not necessarily at a reduced price, which would normally be "In (the) sale".
Having said that, "all items not on/in sale" does indeed mean that no items are on/in sale, and should be avoided if the real meaning is "not all items on/in sale" (or "some items not on/in sale").