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I just checked mine, yes it does have a slight bit of play when zoomed out.
Lightroom doesn't support lens correction on the XZ-1 unfortunately, although someone on DPR has created their own which is supposedly quite good. Have a search in the Olympus forum over there for more details.
Enjoy the camera, it's a great little compact.
Thanks for checking.
I'll have a look over at DPR for sure