Most of the criticism surrounding Martyn's reconstruction seems to have centered on his appeal to the Birkat ha-minim (the Heretic Benediction). Raimo Hakola ("Identity Matters: John, the Jews, and Jewishness") has recently extended the critique in new directions by suggesting Martyn's proposal does not harmonize with new research on early Rabbinic Judaism. In general, Martyn's theory rests on a picture of the Pharisees exerting extensive control of Jewish society after the destruction of the Jerusalem temple in A.D. 70. Here are Hakola's specific critiques:
1) the Pharisees had little control over synagogues during the period the FG was written;
2) documentary papyri from A.D. 70–135 reveal the average Jew was not greatly influenced by the Pharisees;
3) the Temple authorities, not the Pharisees, were likely the main enemies of the Johannine community;
4) the rift between Jews and Christians was not precipitated by Christological beliefs but because of differing attitudes towards central symbols of Jewish identity (i.e., the Torah, the Sabbath).
I am far from an expert on second-temple Judaism (frankly, I'm no where near an expert on the Gospel of John either). That said, I will give others the opportunity to comment on Hakola's first three suggestions. Regarding Hakola' last suggestion, it seems problematic on at least two-levels. First, Hakola himself (like Martyn) adopts a "two-level reading" of John that sees the FG reflecting the situation of the Johannine community rather than the life of Jesus. Second, Hakola's suggestion does not provide a satisfactory explanation of the Evangelist's "replacement theme" (Jesus as the fulfillment of major Jewish religious symbols such as the temple and Passover).
Any thoughts . . .