Half of the times I have problems while logging in with Google. It shows me the web view inside the app (see the screenshot below).I tried reseting the app, deleting the app and reinstalling it.
iPhone app login issue
trello
There was a bug in Trello that broke part of the iOS login process; instead of directing you back to the app after logging in with a google account, it would leave you in a window showing the mobile version of Trello.com.  It should be fixed now.