If you are using a self signed SSL then the login failure happens. For now, please use relay and https (https://yourid.tonidoid.com) for now. The next iphone app in appstore will also handle self signed certificate.
There should be no other login fails. If your iphone browser can access tonido, then the iphone app will also be able to access your tonido as well.
I have the latest version on my PC I just downloaded it 4 days ago. I just can't get the iPhone app to connect. My password and log on are good because I can log on with safari. I don't want to order a Tonidoplug unless I can get the app working.