I think this is a great example of tricky it will be to define what is and what isn't on-topic. I completely agree with you when you say that "skepticism is a pair of glasses you should preferably always wear when looking at the world." The scope of the site shouldn't be limited to known pseudosciences like homeopathy, intelligent design and astrology. If we do agree on that, though, we'll need some criteria other guidelines to determine what is or isn't on-topic. Otherwise, the scope of this site would be, well, everything.
That is, I think should cover the basic questions on science that are propagated by non-scientists (Al Gore, Jenny McCarthy, mainstream media, etc.) and hearsay ("you get a cold from being cold" and the like), but we leave the real questions to the real pros (i.e. Physics.SE, Biology.SE, Chemistry.SE, etc.)
By those guidelines, "Is it dangerous to have several vaccines at the same time?" is on-topic, but not all medical questions will be.
On the other hand, question around the lines of "Is there a substantial difference in rehabilitation therapy and expected outcome for a hemorrhagic stroke patient versus an ischemic stroke patient?" would belong elsewhere. They're too technical and thus beyond the scope of this site.