OK, so what "can" we do? If we believe the rumor, one of the pilots typed a "2" instead of a "3" and nearly spread a 300-tonne mixture of passengers and kerosine all over the end of the runway.
Thats flying man, thats flying. There are hundreds of other opportunities to make tiny errors that can have catastrophic results as well. Entering in the weight on he FMC is just one. Many are shocked to find out that a simple mistake like that can result in a major crash, mind you, often they're the same people that think pilots are just bus drivers.
How about we get the ARRIVING crew to enter the estimated settings for the next flight before they leave the aircraft?
The next crew haven't planned the next flight, they don't know the weight of the aircraft for the next sector. They don't care too much about it either as it isn't heir flight. The fuel loads and pax numbers change quite a lot sometimes.
The best way to reduce this kind of thing is having excellent crew layover conditions, good HF training, fatigue management teams/systems, and if it's a turn around then make it long enough so that the crew aren't under pressure.