Okay, after I've finally gotten rid of an annoying problem, the tile stability display works. I've used the same color code as the wiki's stability maps, so that there are now five categories:
Core Area: No penalty, but you mustn't allow enemy cities here.
Historical Area: No penalty.
Unstable Historical Area: a historical plot that happens to be in another civ's core; expect instability and possible revolts.
Foreign Area: Expanding brings a penalty after a tolerance is exceeded.
Foreign Core Area: a foreign plot that happens to be in another civ's core, worst possible stability.
Edit: I just realised that screenshots don't include the cursor. It's above England, Ireland and Netherlands, respectively.