I respectfully and politely disagree, partly. I'm playing in a Mongoose game now. The task system is fine -- it works*.
On the other hand, I find that their skill improvement rules distract from the game. They have essentially introduced a form of "leveling up" fully into the game. We're all tallying up weeks in training, waiting to level up a skill.
This fills an empty place in many people's minds. But Traveller ignores leveling up on purpose. I feel that adding it back in appeals solely to gamer twitch -- it sure does me. In the long run is at best value-neutral, and at worst moves Traveller towards a pale variant of Star Wars / D&D / Pathfinder / Whatever.
MAYBE, MAYBE that leveling up mechanic introduces some sort of interest in "what to do during jump". But, I think it's the wrong approach. In other words, it seems to me that the solution does not fit the need.
* Although I worry that the precomputed task bonuses are not as great an idea as they first looked... due to the essential nature of re-computing that bonus as characters take damage. Introduce another table? Eh.
I went kind of a different way. 3 skills per term, first skill is Skill-0, set skills as broadly as possible then note what the character is familiar doing with the big wide skill. Then use the Instruction mechanic from LBB4+ for the character to work with new equipment/familiarity, they are skill-0 until they work with/practice on the new stuff.
Gives em a sense of learning/empowerment during gameplay but not really crazy since it's all in their skill range they have already.
Then they can do fast Instruction as means to improve fast, but it gets MUCH more difficult going from Skill-0 to Skill-1, moreso Skill-1 to Skill-2, and getting a sensei for Skill-3 that has Instruction-4/Skill-4 is going to require impressing/questing not money and time.
Also have the Eureka skill improvement, but that's risky as heck.