How can I fix/polish a slate tile imperfection after it has been laid down and grouted?
Let's start by saying the tile should be replaced. It still can be replaced even though the grout has been applied. I would insist on it.  

There is little that can be done to repair the flawed tile, except sanding or grinding down the flaw. This would have to be done with extreme caution in order not to scratch and damage the area around the flaw. Perhaps a small stone on a Dremel tool might work if your careful. I doubt you will remove the off color, however. Hopefully the overall finish is a matte finish, because you probably could not bring it to a high polish finish without specialized tools like granite cutters use.