There are certainly many unanswered questions in science. It's why people like me have jobs. However, ghosts aren't an unanswered question- they are just an idea some people have put forth then time and time again failed to produce any evidence to support. There isn't some indication that they exist but with lots of unanswered questions about the details- there's just lots of wild speculation (with absolutely no supporting evidence) by people who don't seem to even know how to put forth a scientific hypothesis, let alone test it.

As for not being able to observe certain things, while we didn't have the tools to observe the details of certain things in the past (and that's a never-ending process), we still could certain observe the overall effects (by virtue of those things being able to effect us). Science progresses through the identification of phenomenon that are not adequately explained by existing scientific theories. However, for this to happen you first need to actually observe such a phenomenon (and not in a "check out this shaky-cam footage!!!" kind of way), then rigorously test ways in which existing theories might explain the phenomenon. And if all the existing theories then fail to adequately explain it, only then do you get to start on the real challenge of trying to come up with novel hypotheses on what might be going on.

However, people making claims about ghosts rarely seem to have a phenomenon to observe to begin with. Then in the cases where there may indeed be such a phenomenon and it's rigorously tested it seems that invariably the phenomenon either can't be reproduced under controlled conditions, or it ends up being explained just fine by existing scientific theories (or it's just some douche-bag in a rubber mask who would have gotten away with it if it weren't for those meddling kids). And after going through this dance time and time again, there comes a point where giving any meaningful consideration to every idiot's claim of "ghosts!" when their house is just settling really isn't worth anyone's time.

Well, when a tool gets developed that's capable of collecting evidence of phenomenon that existing theories can't explain and that some theory about ghosts can, then we can start seriously discussing the matter. But as long as the noise being generated just amounts to "There may be ghosts out there, but we just can't detect them yet", any discussion about them is about as pointless as a discussion about the color of Russell's teapot. Not to mention if we fast-forward 1000 years, and it turns out that despite all the new tech there's still no evidence of ghosts, I'm sure there will still be people making the exact same claim. There comes a time when, barring dramatic new evidence coming to light, it's time to stop giving serious consideration to something for which evidence has repeatedly failed to be produced. And for the topic of ghosts, that time passed quite a while ago.

That millions of people were observing whatever it was they were observing would be a readily observable fact. The details of just what people were actually observing, determined through controlled observation, and putting forth and testing hypotheses on just what was occurring- that would be science.

Hi, professional scientist here (chemist). First off, what science actually involves is identifying an observed phenomenon, putting forth a predictive, falsifiable hypothesis that would explain the phenomenon, then putting that hypothesis to the test by seeing if the predictions it makes actually correspond to what is observed in experiments designed to test those predictions. Second, regardless of how many experiments and observations are consistent with the hypothesis it's still never proven (although after numerous such experiments the hypothesis will be regarded as having very strong supporting evidence, and it's predictions will widely be used towards practical purposes). Third, such a hypothesis can be disproved with only a single experiment; however, as long as the limits and where the hypothesis fails are understood it can still be useful (Newtonian mechanics has been disproved, but is still quite useful as long as it's used within the conditions where it's predictions are still valid). And finally, absence of evidence can serve as evidence of absence, provided there's enough of it. If I simply make the claim that rodents of unusual size don't exist because I've never seen one, that's not particularly strong evidence. However, if thousands of people scour the world over several decades looking for them and they all come up empty, that's much stronger evidence towards the hypothesis that they don't exist. Of course, that hypothesis could quickly be disproved if a rodent of unusual size suddenly jumps me, but that just goes back to what I said earlier and is precisely how science works.