Very interesting. First of all here's a youtube video associated with the paper -- https://www.youtube.com/watch?v=M2IebCN9Ht4 . Second some on here have posted about the Svegedy, Goodfellow, and Shlens paper http://arxiv.org/abs/1412.6572 which discusses the opposite effect. The Svegedy research is mentioned in the Nguyen paper and specifies that given an image that is correctly classified in a DNN, you can alter that image in a way imperceptible to a human to create a new image that will be INCORRECTLY classified. The Nguyen, Yosinski, et al. work that's the subject of this post states that given a DNN that correctly classifies a particular image, you can construct a gibberish image that the DNN will classify as the same image.
Both results are interesting from the point of DNN construction, and there have been some papers suggesting ways to counter the effects specified in the Svegedy research. In practice (as others have mentioned) in order to construct an exploit similar to the one described in this post, you'd need to have a lot of knowledge about the DNN (e.g. weights) that an external attacker wouldn't have.
What this does leave open, though is a disturbing way for someone with internal access to a DNN doing important work (e.g. object recognition in a self-driving car) to cause significant damage.