Many times here, we have noted the common error of those who take similarities in theme and practice from one source to the next, in assuming that this means that the later source or sources are inventing history. We have seen this in The Homeric Epics and the Gospel of Mark -- a work now fading into deserved obscurity -- and in Randel Helms, and it is likely that Thompson's work will also sink the same way, for it makes the same sort of errors, only this time, mainly with the Old Testament.
Thompson is rather evasive about whether he is promoting the idea that Jesus never existed, was crucified, and so on. Indeed he repeatedly declines to answer questions about historicity. To set the stage, though, we remind readers of this exemplary statement we have used often, by oral tradition specialist Albert Lord:
Traditional narrators tend to tell what happened in terms of already existent patterns of story. Since the already existing patterns allow for many multiforms and are the result of oft repeated human experience, it is not difficult to adjust another special case to the flexibly interpreted story patterns....The fact that the Entry (of Jesus) into Jerusalem, for example, fits an element of mythic pattern does not necessarily mean, however, that the event did not take place. On the contrary, I assume that it did take place, since I do not know otherwise, and that it was an incident that traditional narrators chose to include, partly at least because its essence had a counterpart in other stories and was similar to the essence of an element in an existing story pattern....That its essence was consonant with an elements in a traditional mythic (i.e., sacred) pattern adds a dimension of spiritual weight to the incident, but it does not deny (not does it confirm, for that matter) the historicity of the incident.
Messiah Myth is, essentially, an exercise in violating Lord's cautions again and again, and assuming that the use of existent patterns somehow makes Biblical (and other, secular) accounts fictional. Couple this with Thompson's neglect of serious NT scholarship (as for example, his claim that the Gospels are not biographies  and that scholars only "assumed"  oral-traditional backgrounds behind certain texts), and add in a good mixture of the sort of vague generalization plied by copycattters ranging from McDonald to Acharya S, and Thompson has all he needs to declare every sentence in ancient history fictional if he so desires.
Part of the problem with Thompson's thesis is that indeed, he stretches for parallels and uses "logic" that resembles something out of Lloyd M. Graham or Alvin Boyd Kuhn. He makes much, for example, of Matthew's re-use of themes from the OT, and concludes from this that, "Neither Matthew nor Mark suggests that Jesus speaks within history. Nor do they offer an account of their prophet's own thoughts or expectations." 
So if Matt and Mark can "use stories as parables to deal with well-worn theological issues" then why can't an actual prophet named Jesus have done the same?
Another example  has Thompson making the cloud Elijah sees on the horizon (1 Kings 18) as a "contrast...to the roaring voice of a Baal-like storm God" which "reintroduces the tension of the opposition of the destructive voice of divine wrath and the gentle , supportive voice of the rain's life-bringing blessing."
Really? Thompson's explanation is the sort of creative interpretation we'd expect from a Goth poetry reading; but as an exegesis of the text, it scores mainly as advertisement for an imagined secret message. Sadly, the closest this method comes to that of a past opponent is in the Roman Piso theory which turns the book of Acts into a secret travelogue of favorite Roman brothels.
Thompson shows no awareness of the ancient mind which dealt with and described things in terms of prior experience. Imitation, in this paradigm, does not determine historicity; evidence and plausibility does, as it does in standard historical study. It does not occur to Thompson that Jesus' feeding of thousands in the wilderness is an enacted fulfillement by a real, historical figure of Ps. 78 and the question of whether God can lay a table in the wilderness. It does not occur to him that numerous sages and teachers in history ought to make (or repeat) statements about the poor, because historically, there have been a lot of poor people around.
In all of this Thompson merely asserts -- he does not argue or prove -- that reading the texts historically "distorts far more than it clarifies"  and assumes that offering variously valid parallels proves enough. Logic like this was what would allow Raglan to turn Lincoln or Napoleon into myths as well, and it is so bad here that Thompson even appeals to Dionysus, Tammuz, and Baal, and misdefines "resurrection" as any reversal of death .
It takes little discernment to see where Thompson comes from. Anyone who decries the Jesus Seminar as too conservative [11!] obviously is too far into letting ideology govern credibility. Though he is a credentialed scholar, he is on the utmost fringe as one of the so-called radical minimalists who regard even the most basic accounts of the books of Kings and Chronicles as pious fiction.