The biggest problems when this happens are (in order of frequence):

1) Airline cannot find a record of your booking if using your passport (incl. a swipe of your machine-readable passport) to try to locate the booking record for an electronic ticket;
2) Mileage credit not posting automatically
3) Immigration-related issues when the country uses an APIS or electronic visa/ETA system.

... but off all those, the mileage credit issue is the one that is the real issue .... while the airline and immigration authorities are used to such "mix-ups" and a quick explanation resolves these minor issues within them.