The walls of a plastic vial with Mercury inside are darkening. What is causing this?
Mercury doesn't react with PET under normal conditions, but mercury vapor will diffuse into plastics.  The diffusion will change the optical density of the plastic in the area where diffusion occurred. 

Here's a link to a nice study where the mercury was doped with a radioactive isotope of mercury.  This doped mercury was placed in a glass chamber which also contained plastic discs held at a known distance above the mercury.  The plastic discs were removed after various times and then microtomed.  The various layers of the microtomed plastic disc were measured for radioactivity.  Analysis of the resulting data allowed the investigators to measure the rate constant for diffusion of mercury into the plastic.

One final point, plastics are sometimes contaminated with small amounts of various impurities.  Sometimes these impurities were intentionally introduced, such as radical chain terminating materials (sulfur is an example) in order to produce polymers with a certain molecular weight distribution.  So while the plastic itself might not react with mercury, an impurity might.  The above link also provides analysis of plastic contaminated with sulfur and finds a much higher mercury diffusion constant in such materials.