I don't know about fallacies, but reading nonsense like this puts me off to take him seriously:
"Even Klingon appears to be outselling Esperanto round here." Unless he wants to appeal to "appears" to justify himself, what does that mean?
"It looks like some sort of wind-up-toy Czech/Italian pidgin." What?
"Natural languages have rules determining what sounds are accepted as forms of what phoneme." He has that backwards. What forms are accepted as forms of what phonemes is what allows to define the rules, not the other way around.
"Esperanto speakers show no agreement about whether it even has such rules." Of course it has rules, how else could speakers understand one another? And it is a fact that they do understand one another, that can be tested empirically. That he was not able to find the rules written down somewhere, or even perhaps that nobody has written them down to his satisfaction, is neither here nor there.
"(And the ones writing to me seem particularly unwilling to agree on whether inter-word glottal stops are compulsory, optional, or prohibited.)" So why doesn't he do some research instead of relying on hearsay? Obviously whether they are compulsory, optional or prohibited is a matter to be found by doing research, studying how speakers use the language.
"But surveys say distinctions like /v/-vs-/w/, /ts/-vs-/tS/, /z/-vs-/Z/, /h/-vs-/x/ are statistically rare, so it's the people who find Esperanto's sounds strange and awkward who are being objective!" [citation needed], as a wikipedian might say.
"This crazed inventory is a splendid demonstration of Dr Z's linguistic incompetence;" Ad hominem. (Interesting that it applies to the creators of Lojban as well.)
"Zamenhof's efforts to disguise Esperanto as Italian by adding final vowels are miserably inadequate." Where did that come from?
"The whole problem is that Zamenhof mistook his own prejudices about "euphony" for a globally accepted standard of phonotactic elegance." He seems to know a lot about Zamenhof's psychology...
"It's pathetic! Zamenhof didn't just give his brainchild a bad phonotactic system; he failed to recognise it needed any!" Zamenhof was not a linguist, and he was working at the end of the 19th century, not today. He did give it a phonotactic system, he just gave it implicitly, not explicitly.
"... and they still look rotten to me." OK.
"Strangest of all, though, is the prefix <mal->, a meaning-reverser like Newspeak "un-"." Newspeak "un-"? Doesn't he know about good old English "un-"?
""Basic English" cut its essential vocabulary to 850 words;" Please.
"Apart from anything else, where would Esperanto be if any of these languages changed their spelling systems?" Is he serious?
"neat but somehow risible" even the things he likes he can't help himself from putting down.
"The actual forms of these inflections (<-os>? <-inta>?) are unconvincing." What?
"Esperanto's phrase structure rules and so on turn out to be hardly distinguishable from the ones Zamenhof grew up with - they're pretty good simple ones, but it's sheer blind luck..." Again, even what he finds good he has to put down.
Anyway, it's hard to take him seriously when he obviously doesn't know that much about Esperanto. For some reason, he seems angry with Zamenhof, Esperanto, and Esperantists. Esperanto is not perfect, it can certainly be criticized, but this rant is not very serious.