I believe science is indeed overlooking paranormal phenomena. Science basically needs proof that something is physically possible by theorems. Paranormal phenomena are basically inexact and are usually reported by laypeople rather than professionals. Science needs proof.
When you consider the range of paranormal phenomena, be it ghosts or UFO's; and when you consider these things rarely witnessed by a group, science must at least be skeptical. However; I must interject and state that due to the sheer number of reports, I personally think the most valid instances should be investigated. In order for this to happen, one would need a university trained scientist to admit an incident is worth investigating. I don't think this will happen due to possible damage to professional reputation.
The scientists that do investigate these occurrences are generally considered practicing a pseudo-science, yet there are many instances that would warrant investigation in my personal opinion. I believe in infinity, but I cannot conceive it. Science tells us space is infinite. If it did end, what is on the other side?
I believe there are more than five senses, and more than three dimensions, but at this point in time I don't think "conventional" science would even consider this.