Would compensation be due or even requested for the following situation? What would you request as compensation?

A family arrived at LAX two hours and 30 minutes before their flight time. When the ticket printed at the kiosk, it had their last name but the first name of another passenger. The error was pointed out to the ticket counter employee who told them it was because they entered the information incorrectly and told them they needed to be in another line.

The family member (not being a seasoned traveler) then went to the other line, which was quite lengthy, to be told their issue should have been handled by the person in the original line and to go back to the original line. After some arguing and requesting a supervisor, the ticketing issue was fixed and the ticket was issued with the proper name. By the time everything was fixed, it was 15 minutes before the departure of the flight and the family member missed the flight.

American is now making them travel standby for all flights (finally getting out today) and has shipped their bag across country twice. The agents at American told the family member that a flight was not available until after Christmas and because the original flight was missed, they could not provide them with a guaranteed reservation unless they purchased a new ticket.

Would the traveler be due any compensation as this was an airline issue?