A Physicist recently told me this story and I think this is very interesting and therefore, am posting it here...

Einstein deserves all the hype he gets.  But gravitational waves are an interesting instance where he screwed up, and let his high status bleed over into arrogance.  He was saved by a conscientious colleague.

Gravitational waves appear in the weak field approximation of general relativity, but early work had not determined whether they still existed in exact results.  Einstein himself did a lot of work on this, and in 1936, he tried to publish a paper in the Physical Review which he proved that gravitational waves could not exist.

He wrote to Max Born:

Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation. This shows that the non-linear general relativistic field equations can tell us more or, rather, limit us more than we have believed up to now.

He submitted the paper to the Physical Review with Rosen as a co-author, and came up against something he had probably never seen before: peer review.  It was sent to an anonymous referee who sent a report objecting that Einstein's maths was wrong.  Einstein reacted angrily:

Dear Sir,

We (Mr. Rosen and I) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reason to address the—in any case erroneous—comments of your anonymous expert. On the basis of this incident I prefer to publish the paper elsewhere.

Respectfully,

A. Einstein

P.S. Mr. Rosen, who has left for the Soviet Union, has authorized me to represent him in this matter.

Einstein resubmitted the same paper to a smaller journal, the Journal of the Franklin Institute, which had no peer review process. 

But before publication something surprising happened: a relativity expert called Howard Percy Robertson visited Leopold Infeld, one of Einstein's collaborators in Princeton, and went over the proof with him, pointing out errors.  Infeld told Einstein about the criticism, who realised he was wrong, took it in good spirit, and wrote to the journal's editor to wholly revise the paper's conclusions before publication (which happened in 1937).  The new conclusion: gravitational waves do arise in the exact solutions too.

What was Einstein's error?  He had arrived at the result that it is impossible to construct a single coordinate system to describe plane gravitational waves without generating a singularity.  But he had not realised that this was a just co-ordinate singularity, and could be made to vanish once you allowed yourself to use more than one co-ordinate chart.

Recently it has turned out that the anonymous referee for the Physical Review was none other than ... Howard Percy Robertson, who realised that Einstein had ignored his anonymous referee's report and went to see if he could convince him in person!

It is possible that this was Einstein's only encounter with anonymous peer review.  He certainly did not appreciate it.  But today, we think of Einstein as the predictor of gravitational waves.  He was their predictor, as the creator of general relativity, the originator of weak field theory, and as the person who published a paper showing that they existed in exact solutions too.  But it was only down to anonymous peer review that his claim is as strong as it is.