It can lead to a big headache. Or it can be nothing. Sometimes the airline doesn't check and sometimes they do. This is rather common with Asian carriers, LCC & other airlines operating in higher fraud areas.
I purchased a ticket for a friend to go from SIN-LAX and to get around it I went to the local SQ office and had then note they have verified me as the card holder and had presented the card. This may or may not be a way to avoid the problem as it will depend on the airline.
If you card number has changed but you still have that physical card you can bring that with you along with the new card.
What airline & route are you inquiring about?