Gosh, how does attacking 3rd parties advance the cause of free speech? Will the payment processors suddenly see the error of their ways? Will the U.S. State Department accept WikiLeaks as a legitimate news organization? No, DDoS will not solve your problems. It will just piss people off and conflate WikiLeaks' questionable behavior with blatantly illegal behavior.

As DanielBMarkham pointed out, it makes people notice.

It raises the cost for payment processors to do what they did. They typically respond to economic incentives. (in other news, it looks like they did see the error of their ways: http://thenextweb.com/media/2010/12/09/caving-to-pressure-fr... )

The U.S. State Department won't care as a result of these activities.

DDoS doesn't solve problems, but it can achieve goals.

It probably will piss people off and it's not the best way to do things.

How are the credit card companies third parties after they have taken unusual action against Wikileaks before the Wikileaks people or organization have even been charged with a crime in the US, let alone convicted? Since they clearly cannot justify their actions as being in response to legal action against Wikileaks, it means that they are personally taking a stance against Wikileaks.