Any time you bring the costumes and jewelry of science into a process, you convey the impression that your study has some degree of scientific merit. Ninety percent of science—including that used in investigations—happens between your ears. No amount of equipment or sciency-looking stuff compensates for bad reasoning. Unfortunately it makes good television.
I'm an engineer. I'm part owner of an engineering company, and I've been practicing for about 30 years. Occasionally my firm gets tapped to do forensic engineering investigations. And that means we have a lot of real-world experience in figuring out what happened. The same mindset applies to happenstance observations that get attributed to paranormal or supernatural causes—with one important exception that I'll get to. You're trying to find things you can observe or measure that are the consequences of various possible hypotheses and thus an indicator that some hypothesis operated. In medicine this is known as "differential diagnosis," but it's all just a variation on the hypothetico-deductive methods devised by Popper and Kuhn.
I'll endorse everything that Axxman300 says. You have a set of hypotheses that might explain some observation, and you want to apply a series of tests to rule in or out those various possible causes. Hence the equipment like CO2 detectors. UFO sightings are harder to deal with because they're one-time events; there's a limit to how much you can measure things and say that they apply to the sighting. Hauntings are more promising because they're usually postured as ongoing events. You can measure things at the site and be reasonably sure they apply to the conditions surrounding the sightings.
The a priori probability of each hypothesis is part of the exercise. This is the part of science that needs a brain. Prosaic causes are the most probable because (duh!) they are the ones that most commonly occur. All the measurement in the world may fail to falsify prosaic causes. But that doesn't let you conclude a supernatural explanation by default. Trying to hold out an improbable explanation by default is a common fringe technique—very bad science. Failing to measure a strong magnetic field or toxic gases or rodents in the wainscoting doesn't mean some mundane cause is still not the most likely.
But people who want to believe in ghosts will tell you that the demonstration with all the measurement has "ruled out" ordinary causes, therefore the cause "must" be supernatural. Of course no, the most probable explanation is still a natural explanation you haven't yet thought of or figured out how to test.
Axxman300 has touched upon the converse problem, the exception I mentioned above. In a forensic engineering or legal investigation, you're testing among natural causes that have deducible consequences that can be measured. This gives science a toehold not only in ruling out but in ruing in various possibilities. For example, if we suspect an explosion occurred, we can deduce that chemical products of the explosive reaction will be present and test for them. If found, this lets us infer that the explosion hypothesis is favored.
But because we have have never had a real ghost to inspect, we can't say what physical, measurable properties are associated with their presence. This means we can't falsify the ghost hypothesis. We have a lot of speculation and supposition regarding ghosts, but these are not facts that inform science. Yes, we can test for some of them. "Ghosts create cold spots," is a speculative proposition. We can measure heat fields with reasonably inexpensive equipment. I have a bunch of highly-accurate, calibrate IR viewers at work, but $200 gets you a sidecar camera for your smart phone that works pretty well. What does it mean if we point it at something and discover that it's cold, and we can't immediately understand why? Do we get to conclude it must be a ghost only because we imagine that ghosts are cold? No, that would be circular reasoning.
That leads to the contrapositive error in hunting supernatural activity. You apply a lot of sciency observation to a suspect circumstance and you come up with measurements and observations that defy your intuition. You find there's a magnetic field in your kitchen and a cold spot in your bathroom, and you can't easily figure out why. People who want to believe in ghosts will just attribute those physical factors to ghosts and suppose that magnetic fields and thermal variance are properties of ghosts and therefore—barring an evident prosaic explanation—evidence of ghosts where observed. This indeed misuses the props of science to wrongly convey the notion that ghosts can be measured. We have no idea whether ghosts generate magnetic fields. (But we do have some idea that strong magnetic fields have a subtle effect on the human brain, hm...)
The misuse of scientific tooling by ghost-hunters relies on the audience not understanding the underlying science of measurement. Even something as unremarkable as a camera can create observations that are hard to explain. Instinctively we believe that cameras are substitutes for human eyes, because that's what camera manufacturers are aiming for. But cameras do not record images the same way human eyes do, and are thus susceptible to measurement artifacts that have a powerful effect on viewers because they combine familiar images with things that are created by the operation of the camera. Paradoxically, ghost-hunting treats the camera as some kind of magical instrument that can see things humans can't, and therefore can see otherwise invisible evidence of ghosts. Again, it's not falsifiable.
For a few years I worked with noted ghost hunter Joshua Warren. He sent me photographs that people had sent him, asking if I could explain what was going on. Luckily photographic interpretation is within my professional (and published) expertise, and it's been a sporadic side hustle for me, for television and so forth. Joshua never sent me anything I couldn't explain, and Joshua was very forthright about that. He was happy to learn things about cameras and film that he didn't previously know, because it made him a better ghost hunter.
The falsifiability trap is best illustrated by a thought experiment regarding the top three paranormal suspects: ghosts, angels, and aliens. Imagine some well-known occurrence like the Enfield haunting. Now the prevailing skeptical view is that the Enfield haunting was just the kids having a lark and fooling the grown-ups. But set that aside for a moment and imagine that your job is to scientifically falsify two of the Top Three and prove that the cause was, say, angels and not ghosts or aliens. You can't do it, because the sine qua non of all those is that they are open-ended hypotheses. Whatever fantastical thing is alleged, and for which you say, "Well, aliens can't do that," there will be some alien-visitation enthusiast who points out, "You can't say that's beyond the capability of aliens." That's when the primary scientific instrument (the brain) kicks in and surmises properly that the hypothesization is based entirely on preconceptions brought to the table. No matter how much you paid for your IR imager, it won't fix what's wrong in your brain.
This is why skeptics emphasize critical thinking. Once you adopt a critical approach to claims, you won't be as easily fooled by junk science no matter how starched the lab coats or how impressive the proton pack.
