The topic has been touched many times in the past. For example, in How to deal with medicine questions and the like, I argued that:
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.
As I said in What should be in our FAQ, I believe Skeptics.SE should be to science what factcheck.org is to politics.
That is, I think we 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.
Basically, there are two steps for a question to be on-topic here:
- It has to be a claim, addressed to laymen, that can be empirically verified.
- It has to be a belief or claim that has at least some notability. Questions like "This homeless person told me there is a unicorn on the moon, and that it's made of waffles. is it true?" are off-topic, for hopefully obvious reasons.
Skeptics.SE could be thought of as Fact-Checking.SE.
The two questions you linked to are on-topic, as far as I can see. The one about teddy bears, though, could be far better written than it is.
As for closing off-topic questions quickly, I agree but we (the moderators) are trying to let the community moderate itself (like it's supposed to be). I'm trying to step in only if it takes a while, or if it's blatantly off-topic. Feel free to flag broken windows, though. In fact, I encourage you to flag problematic questions. We're not all seeing, but we do want to maintain an high quality standard.