Hardcore Henry (2015)

This movie doesn't have mirrors, but it does show video feedback that is similar to an infinite mirror effect, beginning at about 1:02.

After being resurrected from death with no memory, after being fitted with cybernetic prostheses, and other superhuman physical characteristics, cyborg soldier Henry goes to the laboratory of the human Jimmy who remotely controls several physical clones of himself who have been helping Henry. One of the Jimmy clones becomes suspicious of Henry, so he creates video feedback by aiming Henry at a playback monitor. This shows that Henry has a built-in camera that is broadcasting directly to their archenemy, the telekinetic supervillain Akan.