It appears that incorrect (manual?) data entry was the cause in each of the three cases and the error propagated undetected through the whole takeoff process.
What processes are in place to either prevent that happening or detecting that something doesn't seem quite right before the point of no return?
Well, I can only speak for QF, and they way that they do things. It's quite apparent that others do things differently.
Each pilot will work out the data separately. You get the weight from the provisional loadsheet yourself. No discussion, or leaning over the shoulder. If there are extra pilots, they will also work it out the same way, though they won't have access to the main computers, and will do it on an iPad. On the 380 there was a calculated excess runway length, which moved substantially with small changes to the inputs. All you'd look for at this time was for that number to be the same from all of calculations. The pilot flying would enter his numbers into an FMC, and then when the briefing was being conducted the other pilot would confirm that the entered numbers were the same as on his own calculations. Again any extra pilots would make sure that what was entered was the same as the brief, and also within a knot or two of their own calculations. No difference between computers was acceptable, but a small difference between computers and ipads was ok.
The numbers don't really vary all that much for long haul ops, though you did have to be careful of flap settings, as the 380 could actually decide to use any of 3 settings. In jumbo days it tended to be the same for all. But, even then the setting is entered into the FMC as part of the data, and it will object if it then doesn't see that setting actually selected.
The V numbers mentioned in the video are ridiculously different from what was required, and should have triggered a few light bulbs. There was a trainee involved, and perhaps the numbers were similar to what he was used to on a previous aircraft. The 3rd pilot really should be looking out for this, especially on a training flight.
Compounding this will be that if the wrong weight is used for the calculation, the power setting will also be incorrect.