Back in January, when Anonymous started their hacking spree in protest of the take down of Megaupload, those who were involved in the DDoS attacks unknowingly downloaded a trojan that gave the author online financial information and e-mail logins/passwords. When the Anonymous hackers started doing what they do, they downloaded a file that was linked on a Pastebin page that allowed them to carry out the DDoS attack. That linked was somehow changed for a modified program that included the Zeus trojan. The program they wanted to download worked as it should, and the attacks were carried out, but since then the trojan has been stealing all of their information. You can read the full Symantec report here.
While the irony is hilarious, this does show a hole in the way Anonymous works. If the government wanted to stop the group, they would simply have to do the same thing as the people behind the Zeus trojan did. The government could modify the program to send the IP and MAC addresses of the people using it to a central server, and from there the people could easily be found. I'm sure the government could hide behind the Patriot Act to make that legal.