Firstly, nice idea for a thread. It's good that you happen to make threads in this section, here and there. After all this time, the Paranormal section doesn't even have two full pages of threads yet. So a new thread is always a plus.
Secondly, at getting to the matter at hand, sometimes proving or even believing in Paranormal activity seems to be near-impossible (but more so proving it. Believing is only hard for some people). Just like religion, Paranormal situations have two or three types of groups. There are believers and non-believers, some who are in between/indecisive (maybe even more groups that that).
I always felt that proving certain things, such as seeing a ghost, UFO, or anything along the lines was impossible. Firstly because I don't believe the stories easily. Ghosts and spirits are probably the only paranormal things that I can find myself believing in, sometimes. As for everything else, I don't really believe in it. And when I see videos that try to prove these things, it makes me doubt them even more (especially when the videos are for entertainment purposes).
It's kind of like what you mentioned. The investigators on those shows who go into a house and experiment and all/check out the house. They have the little night-vision cameras (with the green lights) and walk around with people, hearing weird noises and all. Those shows seem so fake and scripted to me, that it furthers my disbelief in paranormal activity. Maybe, if there weren't as many television shows like the ones I'm trying to describe, I would believe a bit more. But each time I see one, it just makes me doubt it (I realize I said that a few times). It's like they're trying to convince you to believe that it's real, by entertaining you. Maybe if another approach was taken, as to proving that some sort of paranormal activity/being exists, then I wouldn't be so skeptical and instead would believe.
Unfortunately, or perhaps fortunately, that's not the case.
As for whether or not I think paranormal activity deserves investigation... my answer is no. However, it wouldn't bother me if it was investigated. People just need to try a better approach to making it more convincing. Most of the documentaries I've seen are a lot like "The Real World". Sure the people may act as though stuff is real and serious, but how much do you let yourself believe, especially if the show is meant to entertain more than it is to inform?