It's the corner of the carpet on the floor tile - the one farthest from us, not the one in the foreground of the painting. I work in film and one thing cinematographers love doing is shooting into mirrors, so I've gotten used to checking them for continuity purposes :)

As for the dimensions of the room, being 'wrong', that may be deliberate. Again in film props and furniture are adjusted out of their natural position surprisingly often, in pursuit of aesthetic harmony. If you analyzed an interior scene that had been shot from multiple angles in hopes of mapping the room's contents accurately, you'd be disappointed to discover that many things had changed position by ~10% of their own size from shot to shot. Part of the craft is the ability to look at the image on a tiny monitor and be able to identify whatever it is that is distracting your eye from where you're supposed to be looking, like a table which looks fine in one shot but feels too small following a change in the focal length of the camera lens for a different shot. Solution - move the table towards the lens a bit.

Don't even get me started on lighting and related tricks, which can further mess up your spatial intuition. For example, a very common and cheap effect is to make a room feel bigger by painting adjacent walls slightly different shades of the same color. Lots of these techniques are stolen from painting, where the deliberate falsification of perspective has long been used for both aesthetic and semantic effect. Check out this especially famous example: http://en.wikipedia.org/wiki/The_Ambassadors_(Holbein)

The better question is what is the mirror reflecting in the Vermeer?

Yup, looks like his feet to me, as well as the feet of his desk. He seems to facing sideways (to the left)