Since the Zattoo app version 1.5.3, there is no button for full-screen mode. Please use the screen rotation option.
Additionally you can also zoom the picture with double click on the screen.
If you do not receive the full-screen mode after rotating the screen, please check whether the orientation lock is enabled on your device. Swipe the screen from the bottom upwards to display the Control Center (this is possible on any screen including the lock screen). The orientation lock button is located on the right hand side. If the button is highlighted, this means that the lock is active. In this case, please tap on the icon to unlock the screenlock. Now it should be possible for you to obtain full-screen mode in the Zattoo App simply by rotating your device.