Dielectric polarization is not the same as the accumulation of charge.
An electrically neutral dielectric might be polarized but stay neutral. If you put a neutral distilled water between the plates of a flat capacitor and then charge it up, the water would polarize: water molecule dipoles would align in such a way so that the negative Oxygen end would point towards the positive plate of a capacitor and vice versa for the positive Hydrogen end.
On a larger scale it would seem that there is a charge separation present: the layer of water immediately adjacent to the positive plate would have a negative charge (because of all those Oxygens turned that way), and the layer adjacent to the negative plate would have a positive charge. So here's polarization.
But the water would still remain net neutral: there have been no introduction of any charges.
In everyday life, well, you might rub your cat with your sweater and then place your hands on your pet and get electrically shocked. That was an actual separation of charges (while rubbing one dielectric by another - some extra positive charges appear on one of them and negatives on the other) that led to an accumulation of charge - and then the discharge. Same might happen not only with dielectrics, of course.
I can't think of any other particular case, but I hope you get the idea. Basically all the cases when electric sparks and sudden current/voltage peaks are not welcome, there might be problems because of that kind of charge accumulation. It might be electronics or e.g. dealing with flammable substances where the occasional spark might cause a big bada-boom or anything else of that sort.