The FAQ says:

"The third chance to catch an incorrect reservation after purchase is to call AA within 24 hours of ticketing. AA allows its agents to correct ‘mistakes’ to reservations within this timeframe without charging a change fee, although cancellations and refunds are not allowed at this point."

This is not true. I recently bought tickets on AA.com and realized 20 minutes later that the return date was wrong. I called AA and they said that it was impossible to change the tickets AT ANY COST until I received them in the mail. They said that while there was availability at the same fare the next day, they said it was likely that this would change when I received the tickets. They also said that should I succeed in changing them, I would have to travel to the airport to get the tickets physically reissued.