What are some examples of media events that have positively and/or negatively influenced the public’s opinion of a government agency?

There are many media events throughout history that have focused on government failings and successes. A particular media-wide angle on such an event can greatly influence the public’s perception of that event.
One place to begin your more in-depth research is at Ruby Ridge. Ruby Ridge is the site of a standoff between the Weaver family at their remote Idaho residence and federal agents from the FBI and US Marshals Service. The standoff began as a final attempt to issue an arrest warrant against Randy Weaver for making and possessing illegal weapons. All prior attempts to have Randy Weaver peacefully surrender failed as he maintained that he would remain at his home and resist arrest. Over the course of the 10-day standoff, Randy’s wife, young son, and a US marshal all lost their lives. The response of federal agents, which resulted in the deaths of two unarmed civilians, has contributed greatly to a belief among a segment of the public that federal law enforcement agencies are aggressive and ruthless in controlling the lives of citizens, particularly as it relates to gun ownership. This distrust can be seen again and again from the siege at Waco to the more recent occupation of the Malheur National Wildlife Refuge in Oregon.
Another event covered extensively in the media is the response of FEMA – the Federal Emergency Management Agency – to the devastation in New Orleans after Hurricane Katrina. The common criticism portrayed in media outlets centers on FEMA’s slow response. Michael Brown, the director of FEMA at the time, defends against these accusations by explaining that he had no authority to evacuate New Orleans. “FEMA had no authority to do that under the Constitution, which clearly establishes a system of federalism in which state and local governments are autonomous governmental entities,” he has since written. The blame, in Mr. Brown’s view, falls on the shoulders of the city’s mayor, who delayed evacuations in spite of recommendations from others, including President Bush. This story, and the perception that FEMA carries a large responsibility in the ineffective response to Hurricane Katrina, has amounted to a distrust among many civilians towards governmental management.
 
http://law2.umkc.edu/faculty/projects/ftrials/weaver/dojruby1.html

https://www.politico.com/magazine/story/2015/08/katrina-ten-years-later-michael-brown-121782