There is definitely some play in the drum body, and the hopper itself sits very loosely on top of the measure but it doesn't seem to effect anything. In my experience Lee Precision products aren't all that precise, there seems to be a bit of tolerance built into them. It generally all works together pretty good though.
As far as running the measure my typical routine is to fill the hopper with whatever powder I'm using for that session, run about half a dozen charges and discard back in the hopper, weigh one to see where I am and adjust the amount as needed. When I'm close I will run 10 charges and weigh the total to see what the average is, then run a half dozen or so and put back in the measure, then run another ten and weigh them to check the consistency. Once dialed in its rare to get more than a couple tenths variance between the ten charge weights, and more times than not they are the same, especially with easy metering ball powder.