Like shark said, it's important to note that Blackfish is put together very well, and is a captivating documentary. However, especially with news outlets with as much clout as the New York Times, you would think the reviewer would take the time to investigate the other side of the story as well.
SeaWorld does need to take some of the blame though, or at least the PR team. While the facts in the documentary may not be accurate, SeaWorld and 42West (the PR agency SeaWorld hired) did a terrible job of presenting their information, and made it far too easy for the film makers to respond.
What does SeaWorld do in response? They haven't completely accepted the fact that their awful financial situation is due in part to Blackfish.
What do they need to do? I believe SeaWorld is stepping in the right direction with expanding its tanks, but a 2018 completion date may be too little too late. I think that, if possible, SeaWorld needs to move up that completion date.
I also believe that SeaWorld needs to take responsibility for Blackfish, and show their publics what they are doing in order to make the orcas lives better. While the larger environments are a good step, a news release is not going to be picked up by the mainstream media (and more importantly, read by Blackfish supporters) unless Blackfish is brought up. Essentially SeaWorld needs to say "We've heard your voices, now here's how we're trying to help."
I also believe SeaWorld needs to center its focus on the many many things the park does for marine life, including its animal rescues, efforts in the BP oil spill, etc.
I could go on and on...
Also, this Rick Munarriz article is a great read from a PR standpoint of what SeaWorld should do
And another interesting article from the Washington Post, but this is a different conversation for a different time