It's been a while now (almost a year?) but even after upgrading to 15.10 GNOME, I still cannot reinstall previous purchases or sync software packages across computers any more like it used to be.
Choosing either of the two options in Software Center menu File, results in these messages in Syslog:
Nov 7 23:38:05 Aspire-V5 /usr/lib/gdm/gdm-x-session[6011]: Activating service name='com.ubuntu.sso'
Nov 7 23:38:05 Aspire-V5 /usr/lib/gdm/gdm-x-session[6011]: Successfully activated service 'com.ubuntu.sso'
Nov 7 23:38:05 Aspire-V5 ubuntu-software-center.desktop[3244]: 2015-11-07 23:38:05,534 - softwarecenter.backend.login_impl.login_sso - ERROR - _on_credentials_error for Ubuntu One: dbus.Dictionary({dbus.String(u'errtype'): dbus.String(u'GUINotAvailableError'), dbus.String(u'message'): dbus.String(u'Can not find a GUI to present to the user (tried with "(\'ubuntu-sso-login-qt\', \'ubuntu-sso-login-qt\')"). Aborting.')}, signature=dbus.Signature('ss')) ()
Nov 7 23:38:05 Aspire-V5 ubuntu-software-center.desktop[3244]: 2015-11-07 23:38:05,535 - softwarecenter.backend.login_impl.login_sso - ERROR - _on_credentials_error for Ubuntu One: dbus.Dictionary({dbus.String(u'errtype'): dbus.String(u'GUINotAvailableError'), dbus.String(u'message'): dbus.String(u'Can not find a GUI to present to the user (tried with "(\'ubuntu-sso-login-qt\', \'ubuntu-sso-login-qt\')"). Aborting.')}, signature=dbus.Signature('ss')) ()
I checked and ubuntu-sso-client is installed...
EDIT: this question is NOT about the discontinued Ubuntu One or similar/alternative sync services! It's about Software Center's Sync feature that allows a sync of installed software packages.
For anyone that none of the options are working for, like myself, you can just delete software center using sudo apt-get purge software-center and then sudo apt-get remove software-center and then reinstall using sudo apt-get install software-center. Once you reinstall it, open it and go into file->reinstall previous purchases and make sure that they are asking you to sign into an account to view that. Do not sign into your old account, but rather go to All Software and search steam again. Click Buy and then make a new Ubuntu One account with a new email, verify it, and then the installation process should complete unhindered!