The decline in mainstream media trust has been going on for longer than the election, however. Trump just picked up on that prior trend and exploited it.
Anyway, there are a lot of examples of the mainstream media failing to focus on certain events, lacking in accuracy, and at times maybe even fudging the facts to push a narrative. I'll just point out a few big ones that were polarizing.
The first example is when NBC edited the Zimmerman tape. This was big news in conservative circles, but most liberals I know of don't know a thing about it. The effect of the editing was to make it sound like Zimmerman reported Martin's race to the 911 operator without being prompted. In the widely-circulated NBC version the conversation went like this:
Zimmerman: This guy looks like he's up to no good. He looks black.
But, in reality, the conversation went like this:
Zimmerman: This guy looks like he's up to no good. Or he's on drugs or something. It's raining and he's just walking around, looking about.
Dispatcher: OK, and this guy -- is he black, white or Hispanic?
Zimmerman: He looks black.
As a Washington Post op-ed by Erik Wemple about the incident stated:
No matter how you feel about Zimmerman, that bit of tape editing was unfair to the truth and to Zimmerman’s reputation, such as it is. Reaction on Twitter and elsewhere to my previous post on this matter, was brutal toward NBC, with many comments suggesting the worst about the network’s motivations, reliability and so on.
The second one has to do with the Oregon militia standoff. Many liberals I've talked with seem to have no idea that someone was killed by federal authorities during the events that took place at Malheur National Wildlife Refuge. But, again, this was huge news in conservative circles. Now, granted, how the shooting occurred could certainly be interpreted as justified by the authorities. But it's also clear that authorities contributed to how the events transpired.