In 2006, I had a great experience with Southwest regarding an issue like this.

I booked an award flight for the following day for my mom (Houston to Amarillo) It was an family emergency situation (very ill grandfather).
The day of the flight, I tried to check in for her and print her boarding pass and I realized that I had made a typo and booked my flight for the previous day. My RR flight has already passed by about 18 hours!
I started panicking because my mom was already packed and about to leave straight from work to catch her flight.
To my suprise and delight- the phone agent was so sweet and easy to work with, she switched the flight for me easily and I didnt even have to worry my mom with the mix up that was my fault in the first place. (No charges, no issues!)
I fly every week and know that I would not get this service on another airline. Thanks Southwest Airlines!