Exactly. This is why you're supposed to detain the note. If you don't, it will keep circulating round until somebody (a bank, a large retailer, a supermarket) gets a hold of it, checks it and follows the correct procedure.
That said, personally I don't bother checking. The notes at work are all checked when they're counted at the end of the day. Frankly, I'm less bothered by the idea of a multi billion pound business losing twenty quid than I am if some old dear loses out through no fault of her own. I know my employer budgets for a certain quantity of fake notes, while households don't.
