The "yellowcake uranium" evidence concerning Saddam Hussein's alleged efforts to get WMD is an example. This supposed evidence was relied on by the Bush administration to sell the war to the public and to the world. One of the pieces of evidence was a document that Italian intelligence sent to the US that later turned out to be forged. It was disseminated multiple times to the US by Italian intelligence. For all we know, it could well have just been a document they planted, in cooperation with western intelligence agencies. It was pretty much nothing more than an anonymous tip too. All used to drum up support for the Iraq War, by both the US and UK. Interestingly, the document made its first appearance in October 2001 - very shortly after 9/11.
The FBI probably used circular reporting in its FISA application for Carter Page. It cited a media report about the Steele dossier, treating the media report as separate corroborating evidence of the dossier itself. Of course, we don't know for certain whether the FBI knew that the media report was only based on the Steele dossier. But it seems likely the FBI would have known, or at the least they were being willfully blind to it. In the worst case scenario, they did it intentionally. And they were doing it with a former UK intelligence agent. We share a ton of intelligence with UK and Australia, so they probably knew about all this too.
If George Papadopoulos was set up in a sting operation, it's not circular reporting I guess but it's another kind of fake predicate. The FBI likely needed some sort of predicate beyond what they had on Trump/Russia in order to justify opening a formal investigation. Once they had an investigation going, it probably enlarged their investigative power and made it into an enduring thing. If it was a sting, they essentially manufactured a predicate. Oddly enough, Italian intelligence is right nearby to the story, since Mifsud was based in Rome. Mifsud was part owner of a university that trained western intelligence agents. Also, a reputable Italian newspaper is now reporting that, ever since Nov 2017 when Mifsud went to ground immediately after his identity went public, he has been living just a block from the US embassy in Rome.