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The cup holder may be a couple different things.
Are you unable to get it to move fully to the closed position, or does it close but spring back open? If you're unable to get it to move fully then there could be something lodged in it. If it will close but not stay closed then it could be happening because something was spilled in it, or it could just be a failure of the cupholder.
Take a close look as best you can from the top and see if there is anything foreign in it. If nothing can be seen then the center console would need to be removed and remove the cupholder to see if anything can be seen from the bottom side. If there are no visible problems then most likely the cupholder will need to be replaced.
The ink on the mirror most likely partially wiped off when they cleaned the glass. This can happen just due to age and using strong glass cleaners.