Usually there will be a little barrel play when the slide is open of any autoloader. What you need to be concerned about is if there is any play when the slide is locked into battery, as this is the most critical part of ensuring reliability, safety, and accuracy. Have your local gunsmith look at it, but if it's shooting OK, don't fix what ain't broke. There have been many problems with the PT111, as you will find if you research it here. My own gun had bad accuracy problems, which the factory fixed, and I now have over 1500 rounds (post fix) through mine without a hitch. Seems like quality is hit or miss with these things. Good luck.
Tom
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A "Miss" is the ultimate overpenetration!