Just to restate in agreement with numerous posters here...
A definition of the physical characteristics of a ghost is needed,
before one can go off looking for ghosts.
Ghosthunters should just follow the normal scientific process,
or else provide lame excuses for not.
I would like to differ a bit with this, though: the normal scientific process often involves an exploratory phase. We didn't know how the body worked, so we opened one up to see what's inside. After enough observations in this new 'field' we were able to start constructing coherent theories. Gallileo didn't have to be conducting an experiment to be making valuable contributions by looking through a telescope.
What the paranormalists have done is what I call 'scientific
ish' in that they're trying to see if haunted locations have some measureable physical feature. If there's a correlation, we can build a theory of some sort. This is not unscientific.
The problem is that there's no good way to build a blinded baseline against which to know if their measurements mean anything more than background noise. That's where their investigations fall apart: there's no "known unhaunted" baseline location that is otherwise identical to a "known haunted" location.
The operation of the machines is based on question-begging: they know the machines record ghosts, because they recorded anomalies at the last haunted house. They know the house was haunted because the instruments recorded anomalies. The circle is complete.
OK: it's not that stupid... they believe they have an independent instrument for detecting hauntings - psychics and mediums. So, they are looking for a correlation between psychic detection and instrument detection. A positive correlation would be meaningful, and would be scientific evidence (not proof) that the instruments could detect ghosts.
The problem with the independent-medium approach is related to the abovementioned baseline problem: the investigators don't have a "known unhaunted" location to use to calibrate against. And even if they did, it would be difficult to blind them to whether they were at a haunting investigation or baseline calibration.
I'd like to add a comment to the suggestion that this can be done by deduction - that is, the technique of exhausting known explanations until you're left with just 'ghost'. This doesn't work, because if you take the same readings to a UFOlogist investigative team, they'd say that it's proof that you found aliens. The religious would say that it's proof of demonic possession. Or Jesus. Depends on who you ask. Everybody has their opinion about what an 'unexplained' instrument measurement means.
This is what's known as the logical positivist approach: you need evidence of something to sustain a theory of its existence, not a lack of counterargument.