Using the Android app, I can cause the site icon and title to become out of sync with the following steps:
- Click on the top icon and select a site. (Stack Overflow for example)
- Click on the top icon again and select a different site. (MSO for example)
- Hit the phone's back button.
Using the above examples, I would see the SO icon, accompanied by "Meta Stack Overflow".
Android version is 4.3 and app version is 0.1.64.