A quick Google search results in many articles which attempt to refute the Kuzari Argument, as posited by R' Gottlieb. For example, this website (which I have not yet reviewed) presents multiple comprehensively sourced refutations.
Some of the arguments (more to come):
Arguments by example against the uniqueness of the Revelation story
There are similar stories of public miracles witnessed by many thousands of people, which are believed by certain religions by not by others. Examples include the Feeding of the Masses by Jesus and the death of Husain ben Ali. Thus we see that stories similar to the National Revelation at Sinai can be invented and believed.
R' Gottlieb responds to this argument by saying there is a qualitative difference between the several thousand witnesses to the Jesus story and the 600k witnesses to the Revelation, but does not explain why there is such a difference.
He also responds that the descendants of the witnesses are not the ones making these claims, ignoring the fact that at least some of the descendants of the witnesses of the Jesus event indeed believe this story.
There are similar stories which affect the character of a nation's culture, such as the multitude of origin stories.
- Gottlieb responds by saying "If a story places the event so far in the past that no records whatsoever survive from that time, then indeed one can make up stories about one's ancestors... But the revelation at Sinai was accepted at a time when many records existed." He appears not to realize that there are indeed origin stories that appear in many records (such as the Sumerian and Greek myths). Perhaps he means that there are no records from the time the origin story is set in, whereas there are clear records that civilizations existed at the time of the Revelation. This is not relevant, as there are no records (other than the Torah, whose authenticity is precisely what we are trying to prove) that the Revelation occurred.
A similar story appears in Joshua chapter 10, which states that the Sun stood still. This miracle would have been witnessed by the whole world, and surely would appear in other records or traditions had it actually occurred. Since it does not, this disproves Gottlieb's argument that such an event would have been remembered.
- Gottlieb responds by referring two three online articles, none of which are scholarly or peer reviewed. In fact, two of his links are dead, and the third is a long rambling thing about Jesus. He also says, "We can argue that even so spectacular an event as the stopping of the sun would not necessarily be recorded." He does not appear to realize that he's just conceded the point - if the stopping of the sun would not necessarily be recorded, then many such events may have not been recorded, thus completely shattering his remembrance argument. He then attempts to shore up his argument by saying it would have recorded only by nations which attach historical or cultural significance to it, which is both weak and, I think, a form of the No True Scotsman fallacy. He finally attempts to respond by questioning the record-keeping of ancient nations, which is both incomplete (since he doesn't provide any facts), and an example of Lack of Evidence fallacy.
Arguments from lack of corroborating evidence
The event of the Revelation, and all the details concerning it, are recorded in just a single source, the Torah. There has yet to be found any corroborating evidence, whether records from other nations or archaeological remains. Thus, there is, in effect, just a single witness, not a multitude.
- R' Gottlieb responds by saying that historical records from that period tend to record only the history of the nation writing it, and thus it is unsurprising that there is no corroborating evidence. This is true, but misses the main point of the argument. In addition, Gottlieb notes that many of the records of the time contain exaggerations and falsifications, without realizing that the exact same argument could be leveled against the Torah.
Straw-Man Fallacy Argument
Gottlieb is arguing against a Straw-Man, that is to say, he's inventing a weak position and the arguing against it. However, he does not address the actual academic theories about the origin of the Torah. Specifically, Gottlieb argues against a single person suddenly inventing the story, but the theories posit multiple people slowly evolving such a story. We have many examples of this type of evolution of stories among ancient peoples, and thus it is not a stretch to posit that a similar evolution took place among the Jews.
In addition, Gottlieb's presentation of the theories against which he's arguing is backwards. The theories do not claim that first there was a story, based on which the people invented religious practices and rituals. The theories claim that the rituals and practices came first, and the story was slowly invented to explain the rituals and practices.
The invention and believability of such stories can be demonstrated from our own (Orthodox Judaism) history. The traditional explanation for Dreidels on Chanuka is that the Jews in Roman times used to play them to hide the fact that they were learning Torah. However, it has been well established that "spinning tops" started as a secular game in Europe, and a "traditional" explanation was later invented to authenticate and Judaize the practice. (Source)
Argument from Lack of Multiple Traditions
Assume, as Gottlieb does, that there hundreds of thousands of witnesses to the Revelation. Each witness, being human and thus subjective, would have had a slightly different experience at the Revelation. More importantly, due to flaws in human memory and differing educational abilities, each one would have told a slightly different story to their children. Even with periodic corrections, over time, this should have led to many different (but similar) versions of what occurred at Sinai, which should be represented either in our records or our tradition. However, a single version of the events is recorded and universally believed by traditional Judaism. This indicates, even given Gottlieb's assumptions, that at some point all the variant traditions were eradicated or forgotten, which raises serious issues on the integrity of both the parent-child tradition which Gottlieb bases his argument, and on the Torah, which records but a single version of the events, thereby eliminating the "multitude of witnesses."
Argument against the Logic presented by R' Gottleib
What about the logical proofs offered by Gottlieb to explain Kuzari? These also wither under scrutiny. Let's look at Gottlieb's main syllogism:
(1) Let E be a possible event: Why are we assuming that an event--any event--actually happened? Whether the event really happened is what we are trying to figure out! We also need to clarify the parameters of "possible," as I don't grant automatically that a god appearing to the multitude is itself a possible event. Finally, notice how we begin here with an event, something empirical, but then move in #2 to something that could be empirical or subjective, and end up in #3 with a purely subjective belief. With every step, the reasoning takes us away from the empirical.
(2) had it really occurred, would have left behind enormous, easily available evidence of its occurrence: What is meant by evidence? If I tell you something and you tell your brother, is your tale considered "evidence"? What's meant by "enormous" and "easily available"? I am not engaging in sophistry by asking that the vital terms of an important argument be made with the utmost clarity and specificity. I have little problem with the phrasing of the principle on its own, but when we apply the principle to Sinai, we need to have the key terms mapped unambiguously to details of the story. When we're talking about Sinai, the fact is that we don't have good evidence and we don't have enormous and easily available evidence. We basically now have only the Torah. If the only evidence is testimony and/or social memory, then the evidence is poor: it doesn't bring us to the truth of what the event might actually have been.
(3) If the evidence does not exist, people will not believe that E occurred: This is ultimately the money statement of Kuzari, the assertion that people won't believe just anything. Some claims are so extraordinary that people will demand to see the evidence, the assertion says. In this way, Jewish belief is supposed to be proof of Jewish belief--hence, we go around in a circle. But the big flaw in much Kuzari-based reasoning on Sinai is the assumption that the story appears suddenly, as if the story itself were specially created by a god and placed in a culture that also was largely static. Claims evolve and societies evolve--both are dynamic.
The evolutionary nature of both stories and societies thus undermines Kuzari's premises. This evolutionary development is extremely plausible and very well attested. I am not here proposing that a band of actual pre-Jews were stupefied before a real volcano (for instance), and that this event was the true and singular origin of the Torah's revelation story. Indeed, if Kuzari were right, then the Torah would the one and only instance in human history of a cultural text emerging fully formed and never, ever changing across the centuries. I am instead proposing that the existence of the Torah report and that the traditional Jewish interpretation are not and never were necessarily credible as evidence.
Argument from Occam's Razor
Let's assume there were 600k Jews in the wilderness, and they witnessed some kind of great event there, with thunder and lightning and earthquakes and whatnot. Claiming that they witnessed a miracle - Divine Revelation - which is entirely unique is the most extraordinary explanation one could give for such an experience. It is far more likely they witnessed a natural event.
In addition, contrary to Gottlieb's claims, it is far more likely for one to believe a mundane explanation than a fantastical one. Extraordinary claims require extraordinary evidence.
Argument against the integrity of our chain of tradition \ Refutation via forgetting "national unforgettables"
In Nehamia, 8th Perek, it is clear that the Jews of the second temple era hear the torah for the first time in many many years, and weep because of their sense of loss.
What happens next is amazing: They learn for the first time about Succos! Now, Succos is supposed to be a remembrance of the exodus.
Moreover, it states clearly that Succos had not been observed since the days of Joshua ben Nun! Since he took over from Moshe, and I don't believe Moshe observed Succos, that would mean Succos had never been observed until the days of the second temple! (I could be wrong about Moshe not observing succos, but it wouldn't affect this refutation of the Kuzari, btw).
Now, if they didn't remember the "remembrance", how exactly did they all collectively (from their "bubbes and zaydes") remember the Sinai experience itself?
And another question, separate and apart from this (and there are lots of opinions that address this question in the gemara and the commentaries, so it is not my main refutation): why didn't the Jews remember where Sinai was?! That would seem to be an important place. The apologetic answer is because God didn't want them to worship the mountain itself. Why, then, do we essentially worship the temple mount and the kotel? Some say the temple mount was sinai. Some say, the location was lost during the initial dispersion.
Refutation by Demonstration of Circular Argument
How do we know that there were 600k witnesses to the Revelation in the first place (or any of the details, for that matter)? From the records in Torah, the authenticity of which is precisely what we are trying to prove. This a circular argument, for it assumes its own conclusions.
If you claim that we know that there were 600k there via tradition, then why don't we know the other details via tradition, such as where Mt Sinai is, or the names of (y)our ancestors who were present, and presumably transmitted their testimony throughout the generations. Fact of the matter is that the only details we know about the Revelation are those that are recorded in the Torah, making the integrity of our tradition on this issue very suspect, and leading to the logical conclusion that our only source is the Torah itself.
Additional arguments and examples can be found at