The experiment, which consists of shining a laser at a target many meters away. The person holding laser lifts and lowers it. When it is lowered, the point of light on the target disappears, because it is obstructed by the land "in the way", due to the curve of the earth.
The experimenter says "hmmm, that's weird!" and then proceeds to conclude that his ingenious experiment was in fact flawed.
There's no way[1] to know that whatever landscape they tried this on doesn't have a subtle upward curve that might just as easily "prove" the flat earth hypothesis.
It's amusing in the context of that documentary because they do a 180 in real time because of the results they get. But just because the experiment showed the correct result doesn't mean it's well designed.
1. No way that a flat earther wouldn't dismiss, there's no way they'll trust say a USGS survey.
Scientists do this all the time. Scientific paradigm shifts take a generation; you have to wait for the old scientists to retire or die, before new theories can displace old ones.
I’m late to the party here, but I recall reading (or watching) about one flat earther devising a somewhat novel, and actually very solid experiment for determining the roundness of the earth. Unfortunately, they thought their methods or testing apparatuses were flawed when the results indicated that the earth was in fact pretty roundish. They’ll be back with a fresh experiment, no doubt, to confirm their pre-existing notions.