Sounds like there has been some sort of confusion or last minute gate/aircraft change, however the problem should have been picked up at the gate. If manual boarding was being done the gate agent would be looking at the boarding/sequence number as well as the flight number, you can input any boarding number and the system will accept it, it is up to the gate staff to ensure the boarding pass presented is correct for the flight being boarded, however like all areas of airlines these days staff are rostered to a minimum and pulled from pillar to post !
One of the benefits of automated boarding is bar-codes on the boarding card, the flight number is input at start of boarding process and if an incorrect boarding pass is presented there is a loud beep and a red error displayed on the screen. Much better system but not used by all airlines as it is more expensive !