The most ignored AP style rule these days:

government, junta, regime
A government is an established system of political administration: the U.S. government.
A junta is a group or council that often rules after a coup: A military junta controls the nation. A junta becomes a government after it establishes a system of political administration.
The word regime is a synonym for political system: a democratic regime, an authoritarian regime. Do not use regime to mean government or junta. For example, use the Franco government in referring to the government of Spain under Francisco Franco, not Franco regime. But: The Franco government was an authoritarian regime.
An administration consists of officials who make up the executive branch of a government: the Reagan administration.

Right now, there are 7,460 references to "Saddam regime" at Google's news site. And that's a drop in the bucket.

I change "Saddam regime" every time I see it, but I think I'm alone in this battle.