The outlet cover I have doesn't sit flush with the mirror. The outlet sits back in. Is there a type of cover that will help with this or do I need to redo the outlet?

How far back in? Can you post a pic?

There are extension rings for single gang wall cases that come in various thickness you can use to fill in the space of the glass.

Sounds like you have an opening in the glass large enough for the entire finish plate to fit through. If this is the case, you can find oversize finish plates and along with the extension ring all should look fine.

If you can remove the mirror, you can replace the ring which holds the receptacle. Sometimes called a plaster ring, they are available in various sizes to accommodate different wall thicknesses.