Fact checking isn't usually too bad in the bigger media organisations; I'm not suggesting anything on the level of detail, say, Wikipedia, demands. What we have now is fine.
Just an effort to report only the facts and then report the opinions as companion/complementary work.
I would be surprised if Wikipedia was, on average, more accurate than the NY Times. You'd have to account for what's knowable in some way, and the timing of what was published.
Fact checking is actually not as good in technical articles. Look at any article that you are knowledgable about, then think about all the stuff they missed in the other articles. I seem to remember a couple of "This Week in Media"s where this was discussed in-depth.