Really nice box. I made some years ago, and used the mitered corners like you did. Mine had the slight gaps like you mentioned, and I used a method I learned a long time ago to make them better looking. Take a round steel rod, such as the shaft of a screwdriver, and rub the corners hard enough to cause the wood fibers to bend and close the gaps. Don't overdo this, just enough to get the gaps closed. This leaves a much sharper corner than can be done with sandpaper.
Tom