The PS4 does move if you press down on it. Is it a problem? No. I made a video to demonstrate the "wobble" issue, and what you can do to fix it.
If you're not familiar with the PS4's wobble, when Giant Bomb did an unboxing earlier this week, they noticed that the console would move if you pushed down on the glossy side. Naturally, in the days before a massive console launch, commenters on neoGAF and Reddit began speculating over what was perceived as a potential design flaw.
You can see in the video that the PS4 does in fact move, but only if you press down on it, which is not a thing I expect most people will do. Even if you feel the need to do so, the console moves so little that I doubt you'd be able to damage it just by wobbling.
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