Download error:disk was full. How do I download more shows?

I assume this is an Apple TV 1st gen. If the disk is full then remove content

I had the same problem. The Apple TV (first generation) was set to streaming, so it being "full" didn't entirely make sense. What's more, it meant that the options to remove content were not available. I finally solved the problem by resetting the Apple TV to its factory settings and starting over. It won't even allow me to choose "Streaming" for setting it up now. So I have it set up as a "Synching" Apple TV.