English teacher here. Articles in English can be really confusing but essentially we use the definite article in this situation because:
- Uniqueness: In most situations, there's only one mirror in a room or a home that's readily available for someone to look into.
- Generality: Similar to "going to the bathroom," "look in the mirror" refers to the general act of using a mirror to see oneself, not interacting with any specific mirror.
And every time, the taxpayer foots the bill. Until the funds start coming from police pensions, nothing is going to change.