I also put a crosspiece at the top, but it's still a good suggestion. I'll wiggle it when I get home. Thanks!
the suggestions below are all workable.
Using a sheet of plexiglas for a back would allow let you see the wall behind the shelves.
Next time around, Woodshop I: Shelves inset into dadoes on the sides.
Dadoes are simple to cut if you've access to a radial arm saw., Just make sure the boards are a tight fit. You won't need any nails or screws, just wood glue to secure the shelves