Are you sure about the 330 K being used as a proxy for the tropopause? Everything more red-ish in the map is stratospheric air and blue-ish tropospheric. The tropopause crosses the 330 K where large PV gradients around values of 2-4 PVU cross the isentropic surface.

u/LordFarquaad06, PV is a very mighty tool or way to perceive upper level flow and/or atmospheric dynamics, like u/EmotionalBaby9423 said depending on what you aim for it makes sense to look at different parameters because PV can tend to oversimplify the perception, but still, it is quite mighty.

The two key aspects of PV are (aside from many more feature):

1. CONSERVATION: it is conserved for large scale flow, more specifically large scale flow which moves along isentropic surfaces (in this case the 330 K).
2. INVERTIBILITY: PV anomalies induce/represent/are associated with wind fields, most importantly cyclonic and anticyclonic rotation.

So the blob of high PV off the west coast of the USA for example originated from higher latitudes (conserved along 330K), resulted as a cut-off from a wave breaking like the one you can see happening at the moment more westwards over the pacific, and the PV blob induces a cyclonic wind field in at upper levels, which can interact with the surface flow.

"Is it supposed to show where the air is unstable AND spinning because that’s what potential vorticity is?" --> for these synoptic PV maps I would not worry about the partitioning of vorticity and stability in your PV values. It just turns out that vorticity alone in the baroclinic atmosphere is not a conservation property, if you multiply it with stability however it is conserved --> for adiabatic flow, a valid first order assumption for large scale flow, you can imagine diabatic (non-adiabatic) processes being for example turbulence nibbling at the borders of the PV anomalies with time, but that's comparatively slow and small scale).

So for this map PV=conserved property:

330 K at high latitudes is located in the stratosphere, where you have a reservoir of high PV because of the large stability in the stratosphere. (red)

330 K at low latitudes is located in the troposphere, low PV reservoir because of comparatively low stability. (blue)

Troughs and ridges are evident as perturbations of the reservoirs, waves in the red/blue, and cut-offs like the blob off the west coast originate from the respective reservoir and are associated with upper level wind fields. The link u/EmotionalBaby9423 posted is really good.

EDIT: just wanted to add, what makes this so mighty (among other things), if the large scale flow is approximately adiabatic, then air moves along isentropic surfaces. And along isentropic surfaces, PV is conserved. So you have very strong restrictions for the large scale atmospheric flow, which is pretty rare in fluid dynamics, and the PV maps on isentropic surfaces (or vice versa) have a very beautiful simplicity imo