I strikes me that a better approach for Iran in Iraq is to work to reduce the violence and do all they can to get the US to greatly reduce or remove it's troops. Once the US is gone, the Shiites with their Iranian backers could move with a free hand against the Sunnis and Kurds. This also reduces the number of US troops on their border. Reducing the violence seems to have more advantages then disadvantages for Iran.
This is a separate issue from the nuclear one. However, it could be the Bush administration is using the claim to bolster it's efforts to isolate or attack Iran.
I'm interested in hearing any thoughts on why Iran would want civil strife in Iraq. Seems counterproductive to me.