We have moved our moodle behind Forefront TMG now, so any attempt to go to http://oursite gets forwarded to the https://oursite - it doesn't do specific files, e.g. http://oursite/login/index.php gets redirected to http://oursite/
When we try logging in to the app (latest version - tested on Android and iOS), entering the full https:// address, it thinks about it then changes the url to start http - which will never work. My colleague who was on the server says there were apache error log lines appearing saying file not found for local_mobile but I told him this was expected (we haven't put the plugin on).
I can arrange a test login if you need to debug this further.