There was absolutely, positively, no such error when the Gregorian Calendar was introduced, if only because there was no change of year in the first place when the Gregorian Calendar was introduced.
The 15-year cycle of the Induction is real enough, but the idea that such an error could have occurred is fairly unlikely, if only because it was never “the Dark Ages” everywhere. The Eastern Roman Empire stood, after all, until well into the Middle Ages, by which time such an error would have been utterly impossible, and, frankly, I cannot really believe that such an error occurred in, say, Rome.
There might easily have been such an error involving dates of some individual province, of course. Records for Britain in the 5th and 6th century, for example, are almost nonexistant, and the dates for the few events we know of can be plus-or-minus fifty years or so.
John W. Kennedy
“Compact is becoming contract; man only earns and pays.”
– Charles Williams