the bending of light travelling through an inhomogenous refractive index,
This is unlikely to be a large factor since, in general, it would even out over the distance. On a really hot day, this may be visible as heat haze, but then it would be really obvious and all you'd see is a blurr.
the bending of light due to the earths gravitational field
This would be really really negligable over 5 meters.
and the effect of the moon on bodys of water
AFAIK canals are tidal so this would again be a very insignificant factor.
He also doesn't say anything about his margin of error which as far as i'm aware is bad practise for "scientists".
I have only looked at his first experiment where he claims to see a man in a boat at a distance of 6 miles. In this case, putting errors on the experiment arn't really very important. To be rigorous, he should give an error on the height of the observation and the length of the canal (if it turns out to be [6 +/- 5]miles we would probably be unimpressed) but tbh, I don't think its really necessary.
I havn't really looked into the experiments yet, but if I were to try to discredit them, I wouldn't start with these things

Remember, the vast majority of science is working out what we can ignore. The physical world is virtually infinitely complex and we simply cannot achieve 100% accuracy...hence we approximate.