In chapter II of Redating the New Testament, "The Significance of 70," Robinson sets himself two tasks. The first is to demonstrate that the passages within the gospels wherein Jesus predicts the destruction of the Jerusalem temple do not necessitate a date for these texts after 70; the second is to demonstrate that certain details in these predictions, as well as the failure anywhere in the New Testament to mention the destruction or even the Jewish War as a past fact, indicates that we are dealing with a corpus that for the most part predates c. 70 C.E.
The first task can be judged to be an unmitigated success. First, there is the observation that properly speaking there is no reference to the destruction of the temple, but rather to predictions of such destruction. Therefore, the initial terminus post quem (time after which) for the composition of these passages is not the destruction but rather the prediction. Second, building upon the work of luminaries such as Dodd and Reicke, Robinson is able to demonstrate that there is nothing in these predictions that could not have been gleaned from reading the Hebrew scriptures. Quite simply, the evangelists need not have known about the events of 70 in order to have written these passages. The evidence is not such that the destruction of the temple constitutes a terminus post quem for any of the gospels.
Robinson is a bit less successful in carrying out the second task. On the failure to mention the events of the war or the destruction explicitly, Robinson probably makes too much of the argument from silence. This will risk leading him into special pleading later, as he will associate virtually any reference in the NT to persecution with that carried out in the last years of Nero's reign...even though explicit references to Nero are almost as sparse as explicit references to the events of 70. Frankly, we need to set this argument from silence almost entirely to one side. About the only place where it will be of significant relevance is Hebrews, but even here it's not really an argument from silence; rather, 10:2 asks why the temple sacrifices continue to the author's day, which is a very clear indication that they continued in her or his day, and thus that Hebrews predates 70, or at least fall of that year. But we're getting ahead of ourselves here, as Robinson discusses the date of Hebrews in chapter VII, not chapter II.
More interesting is the argument that certain details of the predictions of the temple's destruction do not make sense after 70. Here Robinson is on stronger but not insoluble ground. Particularly strong is his discussion of Matthew 24:29-31, wherein Matthew has Jesus state that the Son of Man will come with power and glory and send angels to gather all his elect from the four corners of the Earth immediately following the events that he predicts involving the temple. Robinson's point here is strong: this didn't happen c. 66-73. If Matthew has added this as a prophecy after the fact, then he has added as part of those prophecies something that manifestly was not satisfied. This seems a strange way to proceed. Admittedly, the exact eschatological sequence that Matthew envisions is somewhat opaque here, and it's not entirely clear to me that it was clear in his own mind, but nonetheless the point stands: Matthew seems to be writing about the end of the age here, which complicates any sort of prophecy after the fact. That said, this ambiguity regarding what Matthew expected to happen when does potentially undercut Robinson's argument here.
Probably the best judgment on the matter is to conclude that for the most part the events of the Jewish War have little bearing upon the question of the dates of the New Testament. They do little if anything to establish the earliest possible dates of the gospels, as the consensus chronology tends to suppose, but neither do they do as much to establish the latest possible dates as Robinson would like. When it comes to dating the gospels, one probably does well to hang little on the prophecies regarding the temple.