The iconic photograph of a 2-year-old Honduran girl crying as her mother is questioned by a U.S. Border Patrol agent reached the cover of Time magazine before it was revealed that the toddler wasn’t caught up in President Trump’s zero-tolerance border policy and wasn’t separated from her family.

For the White House, the misrepresentation of the photo and its use on the magazine cover with Mr. Trump staring down at the child is one of this year’s most egregious examples of “fake news” that Trump officials say is intentionally used to try to take down the president.

The widely published photograph tops a long list of news items during the past two years that damaged the Trump administration before being retracted, corrected or otherwise proved false.

Fake news appears to be everywhere and, contrary to denials by TV news anchors and White House correspondents, media watchdogs say the problem is real.

American University communications professor Richard Benedetto said a bombardment of news stories that are biased, unbalanced and often just plain wrong has left the public “shell-shocked” and distrustful of the press.

“There is definitely a lot of bad news reporting going on,” said Mr. Benedetto, a former White House correspondent for USA Today.

The volume of bombshell reports hitting the Trump administration that later turned out to be false is stunning.

Here are a few of the stories that had to be corrected:

⦁ NBC News reported in May that federal investigators had wiretapped the phone of Mr. Trump’s personal attorney Michael Cohen. Hours later, the network corrected the anonymously sourced story, saying the government was monitoring the source of calls but not eavesdropping on the conversations.

⦁ CNN reported in June 2017 that former FBI Director James B. Comey, in testimony to Congress, would dispute Mr. Trump’s claim that he was told he was not under investigation. The story was based on one source, according to CNN. Instead, Mr. Comey confirmed Mr. Trump’s recollection of events.

⦁ ABC News’ chief investigative correspondent, Brian Ross, reported on the air in December 2017 that Mr. Trump directed Michael Flynn, who would become national security adviser, to contact Russian officials during the presidential campaign, which would be a violation of federal law and possible smoking-gun evidence of collusion with the Kremlin. The report sent the stock market into a dive, with the Dow Jones Industrial Average falling more than 300 points.

It turned out that Mr. Trump gave the perfectly legal direction to Mr. Flynn after the 2016 election. ABC News clarified the story and suspended and demoted Mr. Ross, a veteran journalist who left the network seven months later.

⦁ CNN in December 2017 reported that the president’s son Donald Trump Jr. had advance knowledge that WikiLeaks possessed Clinton campaign emails. The report was based on an email exchange by the Trumps on Sept. 4, 2016, before WikiLeaks published the Clinton documents. But the network got the date wrong. The emails were sent Sept. 14, a day after WikiLeaks published the documents.

Hours after it made a splash online and on air, the network issued a correction but said multiple sources provided its reports with the wrong date.

⦁ CNN in June 2017 reported that former White House Communications Director Anthony Scaramucci was under Senate investigation for meeting with the head of the Kremlin-linked Russian Direct Investment Fund. The network later said the story, which was based on anonymous sources, was “not solid,” deleted it from the website and fired the three journalists involved.

Other news stories that Mr. Trump dubs “fake news” do not garner corrections but are misleading or leave out key facts.

During the coverage of the family separation of illegal immigrants under Mr. Trump’s zero-tolerance policy, news reports frequently focused on the detention of children and teens in holding pens or “cages.” The reports hardly ever identified the holding pens as temporary detention locations before the children were transferred to facilities run by the Department of Health and Human Services that more closely resembled college dormitories.

The president bristled at numerous reports in December about his scrambling to find a replacement for the soon-to-depart White House Chief of Staff John F. Kelly, despite a long list of contenders for the job.

“Fake News has it purposely wrong. Many, over ten, are vying for and wanting the White House Chief of Staff position. Why wouldn’t someone want one of the truly great and meaningful jobs in Washington. Please report news correctly. Thank you!” Mr. Trump tweeted.

Americans are left wondering who or what to believe.

“Trump has transformed the bias debate into a fake news debate, which is bad for the media. That’s not something you want applied to you,” said S. Robert Lichter, founder and president of the Center for Media and Public Affairs at George Mason University.

It is also part of a long-term decline in public respect for media and other institutions, but the drop in respect for media has been greater, he said.

“They are seen as charlatans by the people they are trying to protect. That should be scary for journalists,” he said.

A recent Pew Research Center survey found that 71 percent of Americans go into a national news story expecting it to be largely accurate, but nearly as many — 68 percent — also think news organizations try to cover up their mistakes.

Just 21 percent said they have a “high level of trust” in the information they get from national news organizations, according to the poll.

Fake news wasn’t always bad or slanted journalism.

Mr. Lichter recalled that one of the first times he heard the term “fake news” was when comedian Jon Stewart used it to describe his satirical newscast “The Daily Show.”

Appearing on the show in 2003, Sen. John Edwards announced that he was running for president.

Mr. Stewart quipped to his guest: “I guess I should probably tell you now that we’re a fake show. So I want you to know that this may not count.”

Four years later, the Pew Research Center ranked Mr. Stewart fourth on a list of most admired news figures. He tied for the spot with serious journalists such as Dan Rather, Tom Brokaw, Brian Williams and Anderson Cooper.

“The phrase ‘fake news’ has become a catchall term that signifies public disgust with so-called news reporting that is actually agenda-driven, one-sided, cherry-picked or otherwise misleading,” said Rich Noyes, research director at the conservative Media Research Center, which has tracked liberal bias in the news since 1987.

“This has been a problem for decades,” he said. “The media’s undisguised adoration of Barack Obama in 2008 was a further step away from old-fashioned journalism. Now, in the age of Trump, the blurring of news with analysis and hard-core opinion on 24-hour cable networks such as CNN has further destroyed whatever credibility the profession has left.”

Still, Mr. Benedetto, the former White House correspondent, said Mr. Trump went too far in calling journalists — even bad journalists — “the enemy of the people.”

“It’s not that they are against the people, but the fact is the public is not being well-served,” he said.

⦁ Rowan Scarborough contributed to this report.

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