Those flaws are in there because it's a TV show, not a real scientific experiment. While they might be perfectly capable of making a correct scientific experiment (I don't know, haven't seen them do it) that does not mean that it is possible to do while still making entertaining television.
Again, pretty strong words from someone who has not, to my recollection, performed a single experiment for this forum.
It is true that the need to produce the results in an entertainment show limits severely the possibility of showing the hard data found. Almost nobody will look through several pages worth of repetitive numbers showing the scientific basis for their conclusions, few people will sit through a 10 minute presentation of the hypothesis, methodology, analysis of possible sources of error, and design issues of the experiment.
Several attempts of the experiment are made and a few of them are posted in the website, but they are, obviously, a bit boring to see.
And the conclusion is reduced to one word, which is, in my opinion, the worst flaw as far as scientific methodology goes, due to the entertainment nature of the show, but they usually do have the analysis for their conclusions. They also could use much bigger samples, but there is a small cost to benefit relation in knowing the truth about any given urban myth.
So, please go and experiment with a boat leaving port, or track the position of the stars, or measure some distances through a couple of methods, or measure the apparent size of the sun and moon, or design an experiment to measure the bending of light. Or something. Only then you can say others are not doing the scientific experiments they say they do.