I've always been pretty interested in the Titanic, (yes, even before the movie) as evidenced by the fact that I even ventured to click on a link to the science section. I find it really fascinating that even exactly 96 years to the day after its sinking, it is still relevant enough that the Times would publish such a long piece on it.
There are a few reasons for blaming the rivets (well, you know, and the iceberg) for the ship's demise. First is the fact that the Titanic, the Olympic and the Britannic, all sister ships with a very similar and very large, design, were all built at around the same time. Here is a photo of the Titanic next to the Olympia, both in construction:
Each ship required about 3 million rivets, according to the article, and right around the time that the Titanic was being put together was when a relatively bad shortage of "good" rivets occured - meaning that the ship was built using rivets of a lesser quality than would have typically been used. Findings from the wreck show that the high quality rivets that were used were put in the middle of the ship, where it was believed that that most stress would be inflicted. Of course, the iceberg hit the ship on the bow, so having strong rivets in the middle didn't do much good. Another cause that is being suggested is that there was a shortage of skiller riveters at the time, so the work that was done on the ship may not have been up to par with what a more skilled worker could have done.
My favorite thing about this article is the accompanying slideshow, which gives information, provides wonderful images and gives users a close-up view of the rivets in question.