I'm a novice at lock work, but since no one has replied, I'll throw in my tuppence.
IMHO, ideally,there really shouldn't be any play between either the tumbler and the plate, or between the cock and tumbler. However, a little doesn't really hurt all that much.
One fix for the tumbler hole, in the cock, is to file off that extruded metal and using a large ball bearing placed on the square hole in the cock, smack it good to evenly bump metal from all sides to reduce the size of the square. Then file, very carefully, until the cock presses onto the tumbler, with some small pressure.
Both sides of the cock may need this treatment to get it to fit snugly.
As to the play between the tumbler and axle hole in the plate? To my knowledge, there isn't a whole lot that can be done about that, other than welding the hole in the plate and redrilling, or installing a bushing. Installing a bushing will obviously require machining, but is no big deal if you have the tooling at your disposal.
If the tolerance isn't too bad, say not over .010, I would just harden the plate and live with it, unless you have the equipment to do the necessary work.
IMHO, considering the cost of a new lock, I would send it back and buy a Chambers.
I have only used a coupla Chambers locks, but they have only needed minor tweeking to get 'em as right as I know how.
God Bless,
J.D.