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Overnight, TextWrangler crashed with a message "TextWrangler" is damaged and can't be opened. I deleted "TextWrangler" and download it again from the App Store.
I couldn't update from the Mac App Store, because the latest version of TextWrangler requires 10.8.5 or later, so Snow Leopard and Lion users are out of luck.
Since the crash happened at midnight, I wagered a guess that it was date/time related.
Sure enough, changing the system date back to November 11 magically "repaired" the "damaged" app and allowed it to start; while coming back to the present (November 12) made the app refuse to start, with the same message as before.
That's not a tenable long-term solution; but, all is not lost. (See my "fix" in the answer section.)
I'm still curious as to why the app stopped working on a particular day though; and, if there is a better solution that stays "in channel" with the App Store.
It appears that this is more widespread than just the single app..