I've used HMM in a demand / inventory level estimation scenario, where we had goods being purchased from many stores that might or might not be out of inventory of the goods. The sequence of daily demands for these items thus contained zeroes that were legitimate zero demand days and also zeroes that were because the store was out of stock. You would think you'd know whether the store was out of stock from the inventory level, but errors in inventory records propagate and it is not at all uncommon to find a store that thinks it has a positive number of items on hand, but actually has none; the hidden state is, more or less, whether the store actually has any inventory, and the signal is the (daily demand, nominal inventory level). No references for this work, though; we were not supposed to publish the results for competitive reasons.
Edit: I'll add that this is especially important because, with zero demands, the store's nominal on hand inventory doesn't ever decrease and cross an order point, triggering an order for more inventory - therefore, a zero on hand state due to erroneous inventory records doesn't get fixed for a long time, until somebody notices something is wrong or a cycle count occurs, which may be many months after the problem has started.