Math Teachers at Play #29

Jason Dyer at Number Warrior has posted the latest Math Teachers at Play. I like the classic puzzle he included for 29, and the question he asked:

...can you generalize the errors made in the puzzle? Can you give a textbook, not-designed-as-a-puzzle example where this happens?

 I'm not sure how to start answering that, but I hope folks will give it a shot - it sounds like a great conversation could develop around this question.