Can someone divinely inspired make a mistake? The answer can only be yes.
Rava said: Even Daniel made this miscalculation, as it says, "In the first year of his reign, I, Daniel, contemplated in the books" (Daniel 9:2). The language "contemplated" implies that he had erred.Daniel the prophet made a mistake in interpreting the prophecies of Jeremiah and calculating when the Babylonian exile would end.
Similarly, it is well known that R. Akiva supported Bar Kokhba as the messiah. This was clearly a mistake (see my Kuntres Bikores Ha-Ge'ulah, p. 2 n. 5). R. Akiva, one of the sages of the Mishnah, is assumed by many to have been under divine inspiration as a member of the Sages.
This is not to suggest that such people always or even frequently erred. It was unquestionably a rare occurrence. But impossible? Or heretical to even suggest? No.
UPDATE: Grey Area, a commenter, reminded me that the Talmud Yerushalmi (Ta'anis 4:5) states that Jeremiah made a mistake -- that was recorded in the Bible -- regarding when the walls of Jerusalem were breached. It also states that Ezekiel made a mistake about whether the Temple was destroyed on the first or ninth of Av. However you want to theologically explain this phenomenon, the point is that no human being is infallible.