What would be the problem with the trim, beside the initial roll tendency after AP disconnection?
Takata,
The problem with the trim is that it moved to a high aircraft nose up setting without crew awareness.
It appears that a FBW aircraft requires the pilot to know exactly what mode the aircraft is operating in or else the question arises, "What's it doing now?" In the case of the AF447 crew, they had no attention to spare to consider what the trim might be doing, thus the nose up demands caused the trim to run silently to a high setting without the knowledge or anticipation of the crew.
Once at a high setting, the trim acted to stabilize the aircraft in the deep stall that they eventually achieved. When the Captain arrived on the flight deck, he had to puzzle out what he was seeing. From the jump seat, the indications were essentially hidden by the wheels themselves.
The THS autotrim system has virtually eliminated the problem of trim-runaway, but it has replaced that problem with a new set of problems.
With regard to The Shadow's post, I merely pointed to its location. It was a pretty good post considering the date of posting and the breadth of coverage, particularly the human factors. I did not agree with all his points however.