I've found that, in practice, traditional neural networks tend to be prone to overfitting and are finicky about their parameters (in particular the topology and number of nodes you choose).
I use the word "traditional" to describe the NN architecture discussed in the article. Recent NN research has been promising [1], but this article strictly discusses traditional NN's. I don't really have much experience with the newer NN algorithms, so I'm not sure to what extent they suffer from the same problems as traditional NN's.
[1] http://en.wikipedia.org/wiki/Neural_network#Recent_improveme...