score:7
Generally speaking:
You double check with a different source. This makes the most sense anyway; it's unlikely that the answer will change if you ask the same person again (especially immediately). For example, if the counter staff tells you your gate is B6, double check by going and looking at the departures board.
Failing a self-service option, ask a different staff member if possible. Just be sure to ask someone who might reasonably know: the security guard is unlikely to know about flight rerouting options. If you do need to ask the same person again, just be sure to remain polite and patient. Airports are busy places and there's rarely enough customer facing staff to go around.
For something which changes frequently / is time sensitive, such as passengers not showing up and seats opening:
Ask to be put on a wait or standby list as soon as possible, and provide contact information in case you don't hear a page. Airlines want to sell tickets and fill seats, so rest assured that if you're on the list and a spot opens they'll try to inform you. Check again with an agent shortly before the flight or you are about to leave, to verify that there's really nothing available. Do your best to be patient and realize that you might not be able to get on the flight.