I booked a ticket for one of my friends recently and made a spelling error (just one letter) We contacted the airplane carrier to change it but they made such a big deal out of it saying that it is against their policy and that we have to book our ticket again. I know that they ask for Government ID proof when cross checking the ticket at the airport but how big a problem is this?
This is going to depend on the airline. Check-in staff may not notice the error, one letter off, but it may, and insist that the Passenger Name Record (PNR) match the passengers identity documents. Once the PNR is created, nearly all airlines lock the record and, as you discovered, it can't be changed, only cancelled. You might request that a note be added to the reservation and, while it may not guarantee acceptance at check in, such a slight difference might be overlooked, particularly when travelling domestically.