Check-in staff are not always to blame with these mistakes.
When the airline requires that they charge for Emergency Exit seats and nobody is interested the last passengers often get them for free.
Problems mainly arise when the last 20 passengers are 5 families of 4 travelling with your children.
At this late stage seat changes at the gate and on board are required.
The passenger is often allowed their boarding card with the incorrect seat until they get to the gate so that they can complete the security process etc.
It does not take a genius to see why these seats are sometimes mis-allocated. Bad communication to the gate can result in the passengers making it onboard. Cabin crew checks usually pick this up.