Does anyone see double sometimes when looking at a image in the mirror?

It's because you're so close that neither eye is dominating and you're processing both images from different angles simultaneously.

I'm going out further on a limb now, I'm guessing that unlike with most objects, when you're posed in front of a mirror, each eye tends to focus on a different point -- the eye in front of it, due to our brain's tendency to focus on staring eyes, so the effect is stronger. I think other people rarely stand so close and square, staring back, but maybe you could try it as an experiment.

I think it ghosts because your brain still tries to resolve the separate views into one image, somewhat successfully, but less so at the edges where the angles are most pronounced. Is the ghosting similar to what happens when you hold your finger a few inches from your nose?

Of course I might've been describing the wrong phenomenon entirely. There also the issue that with some glass mirrors, your image will noticeably reflect off the front surface of the glass, in addition to the silvered backing, causing a double ghost. I don't know if this is what you meant by it not looking like refraction, though, since this case is due to refraction.