Question Concerning Shelob

About the second or third time watching RotK in theaters I noticed something that has been puzzling me. When Shelob finally corners Frodo and stabs him, isn't Frodo wearing his mithril coat? How does Shelob get through it? (another thing, spiders don't "sting" people like bees, do they?) In case you're thinking that Shelob stabbed Frodo <I>above</I> the mithril, when Sam rescues Frodo, on the shoulder not sporting the wound from the morgul blade, there is a yellow-ish wound, which is from Shelob, that would clearly have been covered by the mithril, the wound being below the shoulder. So anyway, I was just wondering if anyone has an explanation or if I'm just hallucinating.