... also, don't forget to check the passports/ID cards' validity. Should you let through a PAP whose ID is out of date and he/she gets refused access down-route, the airline gets fined by the authorities (and more often than not, the PAP is sent back).
A boarding card count is done at the gate on EVERY flight and has to match the headcount by the Cabin Crew, otherwise... another headcount, another gate check, etc, until it tallies (or until the discrepancy is found to be spurious).
Doing that on your own in 25 minutes for, say, 189 PAX on a 737-800 - not including the inbound and your turnaround duties as a dispatcher? Yeah right...
Cheers