I have been collecting Paul knives for a while. I have them in pretty much all of their incarnations, from the first generation 2P version, then to the 2nd generation Paul II, and I also have a couple of the Lone Wolf models (including a Prankster, one of my favorites). Pretty much all of them, to a greater or lesser degree, developed a tiny bit of vertical play, especially if they get used or handled much. It's very tempting, especially with the larger/heavier Paul II, to 'flip' the knife open & closed while pinching the button between thumb & forefinger. That's pretty much guaranteed to loosen it up over time. At least some versions do have what appears to be a very small hex/torx setscrew set into the end of the backspacer, where it meets the blade in the open position, and I think there's even one on the inside face of the backspacer, to set the contact point in the closed position. I've never attempted to adjust either of them, mainly due to the lack of a wrench/driver small enough to fit it. I'm guessing, in the case of minor vertical play issues, these are probably what the manufacturer adjusts if/when knives are sent back to them.
A friend of mine bought one of the Paul II models at the same time as I did (at a gun/knife show back in the '90s). He used his quite a bit for EDC, and eventually allowed me to re-sharpen it for him. He'd shown me a while back, that the button lock mechanism had actually worked itself completely apart. In the process of cleaning the knife before I sharpened it, the thing did indeed come apart. So I was left with the dilemma of finding a way to fix it for good (hopefully). The mechanism consists of 4 pieces (including a spring under the button). Reassembling it is relatively straightforward, but the downside is once it comes apart the first time, it's tricky to get it to stay together after the fact. It'll keep unscrewing itself, unless it's properly glued/loctited in place. There are maybe 2 - 3 turns of narrow-pitch threading on the locking ring, so there's VERY LITTLE contact area for adhesive to hold onto. Additionally, if any adhesive touches any part other than the threads, you'll end up gluing it open/closed. There's a VERY FINE LINE between screwing it down too loose or too tight, also. The pivot will tend to tighten on it's own when closing, and loosen on opening due to the direction of the threads. Therefore, a middle-ground setting must be figured out before gluing everything in place.
I eventually ended up using Loctite's own version of super-glue (CA type), applied via the tip of a sewing needle to 'flow' the glue drop (only ONE drop) into the seam where the threads are. I'd tried blue, red and green Loctite and, oddly enough, none of them would hold the joint together. I've since learned that Loctite's holding strength is much weaker on stainless steel, per their own specs. The 'super glue' actually worked much better, to my surprise.
The thing that really surprised me, when I first inspected the dis-assembled parts, was that I couldn't see any trace of adhesive or Loctite anywhere in the threads. Not sure what initially held it all together before it came apart. Don't know what kind of 'magic' was used during manufacture.
, but that was OK. I tend to learn more if I beat my head against it for a while. 
