The fact of the matter is that if the MEL guys had followed SOP's, they would have picked up the mistake. Inserting the Take off data in the FMS(C) is one of the most important exercises of the day for anyone in a commercial airline...Your life depends on it...
If you follow company SOPs, any mistake you make with weights will be picked up at one stage in the FMS(C) data entry/ loadsheet verification.
And sorry, if you cut corners you shouldn't be in the left seat or right seat of a commercial airliner.
I don't know the other cases but in the MEL incident, I think millerscourt might be right.