New versions of Mochizuki's 4 IUTT papers (dated 2017-12-14) are available at Papers of Shinichi Mochizuki. Part III includes an expanded Remark 3.12.2 (starting at manuscript page 143) regarding Corollary 3.12 (Log-volume Estimates for $\Theta$-Pilot Objects) (starting at page 133), which has been troubling some experts.
See Peter Woit's blog post Latest on abc and comments thereto.
Progress?
Update
For the record, from the revision history maintained by Mochizuki here, major revisions to Remark 3.12.2 over the last year occurred on:
2017-06-30: "Rewrote 3.12.2 (ii)"
2017-08-18: "Remark 3.12.2, (ii), slightly modified the items "(e^{itw})" and ("e^{toy})" and added items "(f^{itw})" and "(f^{toy})"
Update (2018-09-21)
Back in March 2018, Peter Scholze and Jakob Stix met with Mochizuki and his associate Hoshi for a week of abc discussions. Scholze and Stix concluded that it remains a conjecture and identified specific issues, but Mochizuki sees no problems with the proof. Mochizuki has posted Scholze and Stix' report and his responses on his website ("discussions conducted at RIMS in March 2018 concerning IUTeich"). See also coverage by Peter Woit (where I learned of this development).