If this is for a domestic flight, they are unlikely to care. If it's international, they may cause a bit of a fuss about it, but it's unlikely to be a major problem.

I've had this happen twice - once with Air France for a French domestic flight (they pointed out my error at check-in, said it was OK but don't do it again), and once with Spanair for a flight to Tenerife from Germany.

In Spanair's case, they issued the tickets but could not process my credit card charge due to the name mismatch. They e-mailed me asking me to call them and then they reissued the tickets at the same price with the right order of names.