Spills must be cleaned up, and that's hard because its high surface tension makes little Hg marbles that roll away from the spill to hide in cracks. Still the slope of that equilibrium line on the phase diagram doesn't become infinite at the critical point. Because D vap S is disappearing at the critical point as well, there being no longer any difference between the liquid and the gas. So while the denominator D vap V vanishes, so does the numerator, and the ratio remains finite. Napoleon's cheap white tin buttons spontaneously changed to gray tin in a Russian winter and fell off, freezing his soldiers.
Gray tin is brittle and crumbles under stress.
Thus did the thermodynamics of phase transitions contribute to modern European history. Napoleon's army retreated, literally in tatters, from Moscow. The freezing point would be lowered by adulteration of pure tin in some alloy.