They’re affectionately known as “unchies.” Try that word at your next game of Scrabble!
It’s worth mentioning that an “isolated area” is either an across-word or down-word, but not both. In other words, every single letter in a crossword puzzle is part of both an across clue and a down clue. The puzzle can’t look like a Scrabble game, with words that connect just here-and-there to other words.
Bill Clinton continually did crossword puzzles at his Oval Office desk. The man’s so intelligent, he could work on a puzzle while simultaneously having a high-level, complicated telephone call.
It’s fun when a crossword puzzle’s theme includes fitting an entire word into a single square. For example, the across answer might be LIGHTrail and the down answer LIGHTroom. It can take some effort to figure out the pattern, as it’s normal to expect just one letter per square.
I used to write crossword puzzles for a local newspaper. As the creator, it was too easy to cheat when the words don’t fit like they were supposed to and just put a black box and have the puzzle no longer be symmetrical. I kept my puzzles symmetrical just because I felt there was some truce between the writer and the solver to not do any cheats.
That’s not to say I didn’t get lazy. One of my clues was: 15 Across-Walking backwards. The answer was the obvious:
GNIKLAW
Saw that coming. You get a demerit.
I’ve seen Times and/or Games puzzles with that kind of thing as the theme. It is also standard as part of cryptic clues. However, as a standalone clue it is cheating.
No, that is an unchecked letter. An isolated area is one in which you can complete a segment of the puzzle in isolation, with none of the letters being a part of the rest of the puzzle.
So he could do *three *things at once, then?
Finally, I get the joke in Pratchett. Sator Square is a place in Ankh-Morpork.
Does “regular” = “American”? 
I’m no sort of expert, but it seems to be standard in the UK for both cryptic and “quick” crosswords to have unchecked letters. By way of what seems to be typical examples, I offer the Grauniad’s crosswords.
Yes – considering merely the grids, not the definitions, to a US eye, those look like kiddy crosswords.
Well, I meant regular = non-cryptic. Though we did invent them. 
Having unchecked letters makes the puzzle easier to set and to solve. Perhaps it is done to keep the grids constant and less confusing. The NY Times sometimes runs “Puns and Anagrams” puzzles which are light cryptics in a standard American grid. These long predated the actual introduction of cryptics in the Sunday Times once a month or so.
BTW, so you don’t think I’m a chauvinist, my daughter brought home a Daily Mirror from her ordeal in Heathrow just before Christmas, and the puzzle page is so far superior to the puzzle page of any American paper it is not even funny.
Didn’t someone say earlier that it was possible to solve an American-style puzzle by only using the “across” clues? That says to me that the UK-style puzzles are more difficult, since you must pretty much solve every clue.
(I should mention that this is only an academic point for me; I can’t stand cryptic crosswords! :D)
Now that’s an interesting observation. As a red-top tabloid I’d have expected the Mirror would do a page of pretty easy (even simplistic) puzzles. Hm! {strokes beard thoughtfully}
I’m getting a bit lost. American style, I thought, uses unchecked letters, meaning unless do a Wheel of Fortune-type guess for a few words to fill in the missing letters, seems like you’d need to answer every clue. Or has the American style changed?
That was me about the across clues. An American puzzles (good ones that is) don’t have any unchecked letters.
Here is an example from Yahoo.
You can see various grids here (American, British, Japanese, Swedish.)
To answer the second part of your question, I don’t ever remember seeing a standard American crossword (like one you’d see in the daily paper or the back of your TV Guide) contain unchecked letters.
The Swedish grid doesn’t really belong in this discussion. It’s a picture crossword (a Swedish invention if I understand correctly) puzzle with the clues embedded in the grid and a picture (or more) that generates words or phrases to be filled in. I’d say this is the most common style in Sweden, but there are also British style crosswords.
Ah, okay. Thanks. I see now. When I read about not containing unchecked letters, I envisioned a crossword with no blacked-out squares whatsoever. I’ve seen those before. But these in the links are the ones I’m familiar with, yes.