The fact that it isn't knowledge.
But he has an argument for that. Here:
"But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith's pocket, while Smith does not know how many coins are in Smith's pocket, and bases his belief in (e) on a count of the coins in Jones's pocket, whom he falsely believes to be the man who will get the job."This argument is implicit. He SEEMS to be appealing to the premise
(A) for all p, if a person only believes p on the basis of an inference from premises which are not all true, then that person does not know that p.
Now, one might challenge Gettier on the basis for (A). Perhaps (A) is true, but if it is, don't we infer it from considering individual cases? So, there is a sort of primacy about the fact that Gettier cases aren't knowledge, whereby (A) ought not be used to infer that they are, on pain of a kind of circularity. Nevertheless, this is all very vague, and whatever you think about the proper course, Gettier, for his part, does not appear to be appealing (directly) to intuition in his paper.
EDIT: But let's say we aren't convinced of (A). What might be brought in to replace it? Let me consider two cases.
Case 1. One could simply appeal to intuition---we could say that intuition is sufficient to assure us that Gettier cases are not knowledge. In this case, you want to ask, "does that mean we can trust intuition and it is knowledge?" Well, if we observe ourselves to trust intuition, then obviously we
can trust it. But is it knowledge? Not necessarily. Perhaps, for instance, we trust intuition, and thus are convinced that Gettier cases constitute counter-examples as intended, so that his argument is dialectically successful. But perhaps it nevertheless fails to produce knowledge that Gettier cases constitute counter-examples. Or, more controversially, perhaps it does produce knowledge, despite the fact that it is inferred from premises which are believed but not known. Either way, we will need more before we can conclude that intuition can constitute knowledge. (And more is given in my first reply.)
Case 2. One could appeal to the competency of English speakers. If we take ourselves to be able to competently wield the English language, and if we are able to come to a determination about whether "knowledge" correctly describes Smith's belief, then we should trust our determination. FYI, this is the tack I prefer.
One might argue that Case 2 is actually just a special sub-case of Case 1. One might say that competency as English speakers just amounts to a tendency for our linguistic intuitions to be correct, and that coming to a determination is just an intuition. But although this is plausible, it is not obviously true, and so will require an argument. And in any case, we have seen that even in Case 1, we need more to show what you want to show.