I replaced the Raspberry Pi 1 model A with a Pi 2 model B. The mirror is now stating up at more than twice the speed and the animations of the interface also got a bit smoother.
Because semitransparent mirrors logically don’t reflect as much as real ones, I decided to add some LED lighting behind milk glass inside the mirror’s housing, to lighten up the person in front of it and therefore making him or her more visible.
The light is activated through a button. A short press triggers the light, a longer button press switches between two views of the web interface.