Secondarily, what percent of information we perceive to be facts is actually false across all disciplines?
What percent do you think we will get to before our species is extinct?
“I believe that scientific knowledge has fractal properties, that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe.” — Isaac Asimov
“Space is big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.” — Douglas Adams, The Hitchhikers Guide to the Galaxy
As for "things that we know that just ain't so", it sort of depends on how you define "false". On one level, the map is never the territory, so all knowledge is an imperfect approximation. But if we loosen our britches a bit, and say, that, for example, both Newtonian and Einsteinian physics are still "true" (and will continue to be even as they are superseded by better theories), then I'd say probably about 50%, and that the percentage will stay steady over time.
“The map is not the territory” — Alfred Korzybski
“All models are wrong, but some are useful.” — George Box