B737 Next Generation Undifferentiated
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 98; Flight Crew Type 13000
Communication Breakdown
Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Weight And Balance; Flight Deck / Cabin / Aircraft Event Other / Unknown
Human Factors
After boarding was complete ATC notified us of a 50 minute gate hold. I made appropriate periodic PAs to Passengers. Our wheels up was :50 so I told Agent and Crew to plan to push at :40. At push time no one was ready. I had to go to the top of the jet way to find the Agent and there was no Pushback Crew. As a result we were rushed despite the 50 minute delay. At this point there was a serious chance that we would not make our wheels up time. At the last moment the A Flight Attendant tossed the napkin on to the console and closed the cockpit door. The last digit of the count was illegible and I made the mistake of assuming it was correct. As we approached the runway we were cleared for immediate takeoff. I rang the cabin to notify the Flight Attendants and as we took the runway the A called up to tell us that there was a Passenger that thought he might be on the wrong aircraft. I had the First Officer instruct everyone to remain seated and that we would sort it out in the air. Above 10;000 feet I confirmed the load sheet count of 46 and compared it to the napkin count of 4 (illegible). I contacted the A who said her count was 47. Further investigation revealed that our extra Passenger was a connect for [a different airport] that had failed to exit at the last stop and remained on the aircraft despite the numerous PAs referring to our destination. I suspect that he was in the lav during the through count process. We coordinated with Dispatch to have a [customer service agent] meet him.Slow down; it's always wise to slow down. Also; our procedure of verifying the count as the very last thing to occur before push; seems like there could be a better time to discover this showstopper; especially when faced with a potentially significant delay if an error is detected. Maybe I haven't been paying attention but I ride other airlines and I've never seen flight attendants actually count Passengers before pushback. The potential error chain has too many links with our system.
[Report narrative contained no additional information.]
B737NG flight crew reported they departed with an unaccounted passenger onboard.