I'm not saying all of these tires, or all applications, are unstable, only that it is what I personally experienced in the specific circumstances of my usage and I'm not sure the word unstable is accurate or the most descriptive. These events did not happen in cornering but on straights under hard acceleration (there were changes in grade in most of these situations, but not dramatically). They consisted of the rear of the car oscillating from side to in the rear under WOT, not in an out of control manner, but it would slowly oscillate from side to side completing 3 oscillation in about 4 seconds. I did not notice the traction system interfering at all, but it is possible as it was in track and that remains active in some way though I have never been able to get details, even from SRT, on exactly how the system is programmed to act in track mode. Suspension was in street mode. This oscillating behavior was almost always experienced with relatively fresh pavement (out here, that's mostly black, and eventually weathers to grey or white depending on composition).
The only cornering related weirdness with the tire was in a long sweeping left hand turn that had serious waves and undulations in its surface and the speed was 100-120, mostly at WOT. I would best describe it as a wobble. I did not have the sensation I got with the PS4S in that location and that situation with other tires, even drag radials. I've noticed that the Charger (at least) is particularly sensitive to crossing lengthwise road humps (what I like to call "wake lines" often the results of heavy over loaded truck traffic that squeeze the humps up on either side of the wheel tracks). I don't mean you'll instantly lie in flaming carnage when you cross them, but that the car reacts with a wobble as it crosses from one side to the other and, at least in my experience, the degree of wobble increases with speed. This sensitivity is more pronounced, and in my experience, than in other high performance cars. Now, it should be recalled that I did all this in "street" suspension setting (if I remember correctly) and that and the track traction setting could play a role, I'm not sure.
I don't think any one involved in the discussion is saying that other persons are lying about what happened, or incompetent, poor observers, or whatever. I personally think people are just experiencing different things with some of these tires. Whether those things are artifacts of some manufacturing defects, specific road surfaces, specific climate, or the interaction of the various electronic systems in the car working at varying settings, or a combination of all or some of those, something odd is happening at times. I know I spent ages deciding and researching tires before I picked up that set of PS4S a year or more back, and fully expected them to be exceptional, but I was surprised by how they acted in those specific settings described above. Why that happened, I cannot (and am not attempting to) say, but I am reporting what I experienced. People can make what they wish of all the reports and experiences everyone is contributing. It's easy to come across in an unintended manner and I think we all should remember that none of our fellows on here are criticising or calling into question what people are saying.
That's my two cents, for whatever that's worth.