Imperfect mirrors work very similar to perfect mirrors but their presence is blatantly obvious.
It could be so blatant that a GM simply states that they don't want a game to head in one direction, so they actively deny the input from their players.
It could be more subtle, with a game system providing certain options to the players, with the GM using the rules as a method to justify their denials.
At it's simplest level, an imperfect mirror is a change in the story without illusionism. The players see it for what it is (whether the GM wants this or not). It is the opposite of "Say Yes, or roll the dice...", in fact it is basically "Say No, Don't bother to roll the dice, and now the story goes this way".
Don't get me wrong, not all imperfect mirrors are bad. Players could choose to accept the change in the story's path, following the leadership of their GM...but the GM needs to have earned their players respect, and every time they employ an imperfect mirror, their respect and credibility is put in jeopardy.
I've mentioned a GM named Frank a couple of times in my blog. Frank is known for GM a strict and streamlined game where he puts his players through all kinds of psychological mind-screws. He doesn't hide the fact that he's screwing his players and their characters, but he tells a good story.
I've seen other GMs try to do the same thing, and fail miserably. They either haven't earned the respect of their players, or they've lost it through abusing the power of the imperfect mirror.
Then there are GMs who don't realise they are doing it. Many inexperienced GMs don't understand the concept of player driven stories; as a result they try to lead their players by the nose through a story (or a dungeon) they've created. They don't know how to react to players taking steps off their established path, so they actively block paths leading into the unknown.
Traditionally strict scenario design can be like this as well. Scene 1 leads to scene 2 regardless of it's outcome, which in turn always leads to scene 3, and so on until the predetermined climax is reached.
If a player knows up front that this is the way the game is going to play out, then they can work within this framework. Maybe choosing to explore within, when they know the outside journey has already been established.
Every time I run a game of the Eighth Sea with new players, I tell them that the game follows a strict five act structure. Act 1 will be an introduction, Act 2 will set the journey, Act 3 will consist of overcoming the obstacles of the journey, Act 4 will reach a climax, and Act 5 will deal with the ramifications of that climax. The players know from the start that they will follow this progression within their session. So certain obvious imperfect mirrors are placed in their path, but outside of this act structure the game should be incredibly fluid and character driven. Within that game, I try to ONLY use mirrors as narrative structure.