Lateral balance
With pax moving left or right within the cabin, there is very little change of 'Moment'. Now consider a four engined aeroplane with one engine shut down, - any one, and think how you would manage the fuel panel. Tonnes of fuel are in the wing tanks and the 'moments' most certainly have to be taken into consideration.
As I recall, I have been retired for nearly eight years now, but on a 747 there was no guidance for lateral weight balance in the Checklist or Flight Manual as I can remember, actual limits. My previous experience on C-130s in the military which did give guidance on inter-wing balance gave me suitable knowledge of how to handle the situation when it happened to me on a flight from LHR to HRE "one dark and dirty night in 1996!
It doesn't take 'rocket science', but as an exercise how would you 'Fuel balance' for the remainder of a ten hour sector, assuming the problem occured three hours into the flight.