Taz,
If that vertical play is what I think it is, then it shouldn't be a problem. If you examine the tang that makes contact with the liner, it is not straight and should be slightly slanted. This is to cope with the wear of your liner and designed that way. As I said, it will move to the right side as you use your knife. So the optimum contact of your Genesis is now at the right side as opposed to the left side like when it was new. If you move your liner lock as if to disengage it, surely there's a gap (meaning there's little or no contact) between the liner and the tang, thus the vertical play.
The T-6 screw nearest the tang, like aph mentioned, is very important. You can have side to side play if the said screw is not tight enough. Tighten it too much and it will make opening or closing your knife difficult, because now the scales will pinch the blade. If you see your knife in closed position, the scales (and the liner) have to be parallel to each other. Find the best combination of both smoothness and tightness.
There's an easy way to do this. Loosen/tighten your pivot screw enough so that you have smooth opening. Move the liner to the left as if to disengage the lock. Now shake the knife vigorously side to side, there shouldn't be any side to side play. Tighten as necessary and recheck again.
BTW, Gennies use bronze bushings which contribute to the smoothness. I wish there were more factory knives made this way.
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Reynaert