I don't know of any prediction of the future that was completely accurate. Even 2001: A Space Odyssey has errors. Pan-Am went bankrupt in 1991, the BBC still does not have 12 channels, and HAL is too intelligent for the real 2001.
If you look up "En L'An 2000," you'll see that it is a series of French postcards from the 1900's that depict what the year 2000 would be like. They obviously underestimated how different that year would be like, because they now look like a surreal version of the 1900's.
Futurama is a show created in 1999, and it takes place in the year 3000. Despite the millennium long time gap, it's not removed from the current era, it frequently references things from the current era and before, because it's at least partially a satire of the current era. Maybe since it's a comical satire, it doesn't have to make sense, but I'll go ahead.
I think it would make more sense if it took place in the year 2100. We're at least vaguely knowledgeable about the 1900's. It was a time of the birth of film, and that's the only thing I can think of off the top of my head right now.
On the other hand, you probably have no real knowledge about the year 1000, and I don't, but whatever the year 1000 was like, it was presumably completely removed from the year 2000.
I haven't watched the show in a long time, but I also don't remember the show telling what happened after the early 21th century and before 3000.
