(excuse the crappy flash flare)
I used a lightweight plastic that I found at JoAnne's similar to a shower curtain and then created pockets for the records. The pocket openings are facing the wall so it looks streamlined and like the records are trapped in the plastic but the records can still be easily removed.
I folded the top so that it could handle the weight and added grommets for hanging. As you can see though the plastic is sagging a little bit since the stitch was straight.
Here is a close-up of the zigzag stitch I used
And another angle.
I'm happy with the way it turned out and my boyfriend loves it too. It has a few flaws here and there but it gives it personality.