How to derive a noun from "up-to-date"?

Change it to emphasize the negative:

The document is inaccurate and out of date.

I would use current. Like so:

The document is neither current nor accurate, which caused me a lot of trouble.

You could say "currency". "The document has problems with accuracy and currency." This would be technically correct, but it's a slightly uncommon use of the word "currency", just enough that readers might be confused by it.

I think it would be more clear to say, "The document is not accurate nor current," or "There have been problems with keeping the document accurate and current."

You could try modernity, currency, recentness, or contemporaneousness.