I'm not a linguist, but here's my guess.

Take these sentences where a similar thing happens.

• "Look out the window."
• "I'm heading to the gym."
• "You should hold the door for people."
• "You need a trip to the barber."

In these cases, the noun isn't actually that important, more than it is what you're doing with the noun. These nouns represent the general act of doing something, and I guess since that action is a singular specific thing, we use "the".

This applies to "Look in the mirror." The actual mirror doesn't really matter much. The focus is on the general act of looking at your clear reflection.