Why does my glass fishbowl have a gray sphere inside it, even without an object there? I can clearly see a grey sphere looking thing that doesn't exactly look like a glass bowl. Here's the blender file for the bowl.

I have no idea what is causing this.
Your faces are flipped inside out. Select all faces and press Ctrl+N, to correct this. Additionally, you have double vertices. Select all vertices in your mesh, and in the toolbox to the left click 'remove doubles'.