What could cause a recessed light to come on when removing the neighboring bulb?
If the last light goes out when the second to last is removed, the wiring error may be:


Where electricity travels through the second to last bulb, on it's way to the last bulb.  If so the last two bulbs may also have been dimmer than normal (if they are incandescent).

The bulb type matters here: using CFL or LED lights during testing can add to the confusion.