Mochizuki has commented that he will post revisions of IUTT-III and IUTT-IV "in the not so distant future": kurims.kyoto-u.ac.jp/~motizuki/… . He acknowledges that there is an error tracing back to IUTT-III, which he believes to be completely fixable.

@RH, Ulrich, NB: Thanks for the corrections!

You must add that $E$ does not have complex multiplication (else the representation is abelian, and the conclusion clearly fails). This is rather more elementary than Faltings' theorem (which I don't think would actually help here). See also Serre's Inventiones paper, "Proprietes galoisiennes des points d'ordre fini des courbes elliptiques," for a complement showing that the image equals $\mathrm{GL}_2(\mathbb{Z}_l)$ for all but finitely many $l$.