>> Though the proof has not undergone a rigorous peer review, experts expressed no concern over whether it would survive a critical look.

Such is people's confidence in Terence Tao - not unfounded by any means - but the result has not been peer reviewed yet. Tim Gowers has said that they'll be conservative in their review process [0] so any errors will probably be picked up quickly.

[0] https://gowers.wordpress.com/2015/09/10/discrete-analysis-an...