Without a doubt, Moyes' biggest strength is finding a gem in the transfer market on the cheap. I think that this, more than anything has carried his sides to high finishes in the Prem. The purchase of Cahill, Arteta, Lescott, Jagielka, Pienaar and Baines (missed anyone?) was a great bit of business by the ginger one.
His biggest weaknesses, in my opinion:
1/ tactically inept: negative team selection, re-active i.e. doesn't read the game well enough to make necessary changes before it's too late.
2/ training methods: I can't be too sure of this as I don't attend FF as often as I'd like (maybe never) but our players' technical ability (i.e. holding possession, making clever runs off the ball, one or two touch football, switching the point of attack via one cross field pass, making that 'killer' through ball) is almost non-existent. Our inability to do the simple things right has been most evident on our ventures in to Europe.
At the end of the day, the standard of the Premiership is not very good apart from the top 6 or 7 teams (was 3 or 4 before the emergence of City and perhaps Spurs) which explains why we are so competitive in it, in truth. I believe we could do better with this crop of players but since Moyes ain't going no where, I hold hope that he gets struck by lightning (or maybe Stracqula can bite him in the neck) and changes his ways.