How accurate is American Crime Story: OJ Simpson?

Expecting an exact match between real life events and the series is never going to happen, because not everyone will agree to the same version of events (e.g. backroom meetings, etc.). Jeffrey Toobin, who wrote The Run of His Life, was a consultant on the series and told the following to E! News:

"This series is not a documentary," Toobin, who's a consultant on the series, has explained. "It is not a word-for-word recreation. But in terms of the essential truths of the events, in terms of the insights into the characters, it is brilliant and everyone will learn a lot and be entertained a lot."

This article then goes on to attempt to separate fact from fiction, e.g.:

FACT, for the most part. Robert recalled to Barbara Walters in 1996 confronting O.J., who was looking at pictures of his children and had a gun wrapped in a towel. "In the book it says you said to him,' You can't kill yourself, this is my daughter's room,'" Walters recalled a line from the 1996 book American Tragedy: The Uncensored Story of the Simpson Defense. "I said," Kardashian concurred, "'O.J., I could never walk in this room. My daughter couldn't sleep in this bed, she'd know what happened here.'"

But it also points out:

Nitpicks:

• Kardashian, who's being painted as the voice of reason, wasn't the one to tell O.J. he needed a more hardcore defense attorney and call Robert Shapiro, who's lunching at Mr. Chow when he gets the call in the show. In reality, TV exec Roger King stepped in and called Shapiro, who was actually at House of Blues.
• Marcia Clark had to cancel going to a bridal shower she was throwing, she didn't forget about a friend's baby shower. (It's far bitchier to forget about a baby shower, though.)
• There's video of young Kim and Kourtney Kardashian at Nicole's funeral in real life, but who's to say whether Kris had to scold Khloe and Kourtney for horsing around, telling them to put away the candy, as she does in the show? Hmmm…

It's a long article and there's far too much to reprise here.

Generally it's very accurate, mostly because the writers Scott Alexander and Larry Karaszewski had tons of material to work on:

Due to the high-profile nature of the trial, not only did the production have copious amounts of video footage and media coverage as a base but also most of the main players wrote their own books about the experience. “I think we’re very proud to how close we stayed to the truth while creating drama out of recent history,” says Alexander.

Vulture's review of the season praises American Crime Story's historical accuracy, saying that "devotees of Toobin’s book will be struck by how much inspiration this series takes from his reporting, as well as its overall affinity for sticking to what actually happened rather than embellishing or inventing details — though admittedly, with a case this notorious, what would be the point of making stuff up?" (source)

As mentioned above the show main inspiration was Jeffrey Toobin's book The Run Of His Life: The People v. O.J. Simpson, so in cases where there is no general agreement on the actual events the writers were probably sticking to the book version. Note that the book itself is seen as professional and objective:

The New York Times review extolled the non-fiction work as "a comprehensive, professional account, unburdened by the self-justifications of parties to the case." (source)

That said, there have been some liberalisations of the facts, simply because the story had to be told as a TV series:

Due to time constraints of the 10-hour miniseries, there have been some aspects that were altered. Adds executive producer Brad Simpson (World War Z), “If we’re gonna get dinged, it’s because we have to consolidate things. It’s a dramatic retelling. We’ve consolidated time. We’ve consolidated characters. But in terms of the truth of what happened, I feel like we’ve been really honest.” (source)

For what it's worth Marcia Clark has a very good opinion of the series.