Prior to watching the video, I have a very low estimate of the probability of aliens on earth (intelligent aliens visiting within human history, p ≈ 0.0001, intelligent aliens sending probes of any kind to earth during human history, similar, anything of alien origin coming to Earth over it's entire history: p ≈ 0.1, though I could easily be persuaded of a higher or lower estimate).

We'll see what effect the video has on those estimates.

--After watching the first half hour, taking comments in a window to the side throughout--

"Halt and his team locate three indentations [dramatic pause] in the shape of a triangle" in a very authoritative voice.

"Over two days, 60 personnel reported that they had seen a UFO." How were they asked?

They really like triangles. "my wife and I saw three bright white lights [dramatic pause] in triangle formation". Triangle formation, as oppposed to a line? Either way, it would have sounded significant and ominous.

The original investigation is missing any confirmatory evidence--but that also means it lacks any disconfirmatory evidence. This is exactly what you would expect to see in unexplained cases if there actually was nothing unexplainable going on.

I noted that in the beginning of the video, they mention that most sightings occurred over sparsely populated locations. If events were located in random geographic locations, you would expect low population-density areas to have a disproportionate number of sightings (the probability of a sighting would be a function of the probability of an event, which will be the same everywhere (meaning that it's most likely over a low population density area, as most areas have low population density), and the probability that someone will see the event (which will go up with population density, but approach unity at a fairly low density). If UFOs were hallucinations, you would expect to see a fairly even distribution over population, meaning high population density areas would report considerably more sightings per square mile. In areas that are more dense, such as Europe or Japan, you would expect about the same number of sightings per square mile: likewise with fairly homogeneous somewhat low populations (farming regions) you would also expect approximately the same concentration of reports per square mile. That suggests a fairly informative test: do most reports come from cities, or rural areas. Since, in America, 20% of the population lives in rural areas and 60% live in cities (population ≥ 200,000), you would expect about one quarter of sightings to occur over cities. The effect of disconfirmation from other people in the city who don't see anything would decrease the number of hallucinations reported, but not enough that you would expect rural areas to have a higher incidence of sightings overall.

One other possibility that occurs to me now is that it is possible that there may be a higher concentration of reports near military bases. This would suggest military activities, which are quite likely to A: be conducted near military bases, B: look strange, particularly things like planes flying in formation, and C: be classified.

Phoenix incident:

"In the weeks after the incident [emphasis mine], over 700 reports were called in..." In a city as large as Phoenix, you would expect far more than 700 people to see an object several miles across that remained in place for over an hour. The fact that this includes reports in the weeks after, when people would have asked themselves whether they had seen anything strange, implies that the actual number of witnesses is even smaller. In addition, an absence of better video than grainy shots with home cameras of distant lights is fairly strong evidence against this being a solid object, as per the reports, instead of a number of lights traveling in formation. This was 1997: cameras were fairly decent even then.

You would expect to see much stronger evidence if there was actually a several hundred meter object in the Phoenix shy. High-intensity flares, the official explanation, look like they fit the video equally well if not better, and fit the other observations (silent, in particular) much better.

Remember to compare the convincingness of the report in the video with the most convincing report you would expect to see of something that actually happened, not just an average report of something that really happened.

I don't have time to finish the video, but if there's any piece of information that is considerably more convincing later on (not just more of the same ambiguous information), you could summarize and point me to a 1-minute segment in which they give it.

In the meantime, you could look at the frequency of UFO reports per square mile around cities and rural areas (if the values of reports per square mile are within 1 order of magnitude of each other for low and high population density areas, that's fairly strong evidence for something actually going on) and reports per person in cities and rural areas (if the reports are not within an order of magnitude or two of each other, that's pretty good evidence that this is not caused by hallucinations or something similar). You could also look at incidence per person and per square mile near military bases: if there is a significantly higher incidence there, that implies military activity is the most likely cause.

I don't have geographic data, but if you do and don't know how to run the analysis, I can do that for you.

Result

The video didn't manage to convince me, because I'm fairly sure I could create a video at least that convincing in the absence of any alien activity if I had their budget (and I expect them to be at least as good at making convincing videos as I am).

Amusing sidenote:

This does have a significant impact on my estimate of the budget of the History channel, and my estimate of my own ability to create convincing videos. If I think I can create a video as convincing as a group of experts on making convincing videos on the same budget, that probably means I'm either overestimating my own skill, their budget, or the effect of expertise on making convincing videos.