The good folks over at Nokia Beta Labs have released an updated Nokia Reader client for the S^3 phones (N8, C6-01, C7, and E7). The new release (1.0.1) addresses problems when signing in with Nokia Account and the connectivity issues with the previous version.
You can download the installer file from Beta Labs itself. What should be kept in mind while installation is that there are several steps involved in updating the Ovi Notifications Support Package. So better be careful and follow the procedure mentioned at Beta labs.
PS: S60 5th edition readers do not need this update as the bugs which affect the S^3 devices are not valid for S60 5th edition.