More times than not you can adjust blade centering and bladeplay. Bladeplay is just a matter of tightening the pivot; it takes minute adjustments to find balance between action and bladeplay. Polishing the washers and oiling will improve the action and allow for increased pivot tension to reduce blade play.
Adjusting blade center is more complex. You have to remove the clip and loosen all the screws. Do not remove them. Then you apply tension to the upper side of one scale and the lower side of the other. This will force the blade over to one side. If the blade moves in a worsening direction, you reverse where you apply pressure (lower side / upper side vs. upper side/ lower side).
Once the blade favors the opposite side it originally was toward, begin tightening all the screws to just snug and save the pivot for last. Go back and tighten each screw fully, then adjust pivot.
Pay attention to blade centering while tightening the screws. You may notice once screw causes the blade to move off center as you tighten it. This is the problem screw. Tighten it last and maybe not as tight as the rest.
Keyman has a much better description for this process some where.