What's going on in Trump Tower?

Before going to bed on Monday night, President Trump retweeted an alt-right activist who has promoted numerous conspiracy theories.

When he woke up, the president retweeted a cartoon showing a man labeled "CNN" being hit by a train labeled "Trump." Within minutes, he deleted it, perhaps realizing that the meme portrayed vehicular homicide just three days after an alleged vehicular homicide in Charlottesville, Virginia.

Related: Donald Trump retweeted an alt-right conspiracy theorist. Here's why.

Several hours later, an anonymous White House official told CNN that the retweet was "inadvertently posted."

On Tuesday morning the president also retweeted a Fox News tweet reporting that he's "seriously considering" pardoning ex-sheriff Joe Arpaio, who was recently convicted of criminal contempt by a federal judge.

The strangest moment of the morning came when the president then retweeted a user who said "He's a fascist, so not unusual."

This was apparently an accident, as well. Trump undid the retweet, but the user, Mike Holden, celebrated the sudden burst of attention.

"Donald Trump Rtd me, so he agrees," Holden wrote, confirming that he was calling Trump a "fascist."

Does any of this matter? Well yes -- because every presidential communique matters. Trump uses @realDonaldTrump to share what's on his mind and rally his supporters.

All of his Twitter posts, even the ones he deletes, are covered by journalists, scrutinized by foreign governments and archived by historians.

So it's in that context that some analysts were dumbfounded by Trump's odd posts on Monday night and Tuesday morning.

"It seems almost as if he's working in overdrive to really undo whatever he said in the West Wing yesterday," Washington Post reporter and CNN analyst Abby Phillip said on CNN.

Others suggested that the president was trying to have it both ways -- first he spoke publicly to condemn hate groups by name, but then he retweeted several posts that could appeal to his fans on the far-right.

On CNN's "New Day," former NAACP president Cornell Brooks called the presidential retweet of alt-right activist Jack Posobiec a "racial dog whistle."

Posobiec had attempted to contrast intensive media coverage of the president's response to Charlottesville with this: "39 shootings in Chicago this weekend, 9 deaths. No national media outrage. Why is that?"

Brooks responded: "We see this pattern over and over again with the alt-right, which is to say, whenever there's an instance of anti-black racism and anti-semitism, it's juxtaposed with the so-called 'black-on-black crime.' This is not an accident. The president is again blowing a racial dog whistle."

Tuesday morning's retweets stoked further discussion.

"Fake news can't stop the Trump train!" was the caption on the anti-CNN cartoon shared by the president.

"As soon it was noticed, it was immediately deleted," a White House official told CNN.

The official did not respond to questions about who actually hit retweet on the image. But Trump's social media account is primarily controlled by Dan Scavino, the White House director of social media and an assistant to the President.

Scavino did not respond to a request for comment.

After it was removed, the user who had been retweeted wrote, "We've become so PC, people can't even enjoy humor anymore. Gone are the days of #WileyCoyote."

Some journalists thought it was troubling, not amusing.

"I can't believe this is an image the president is promoting," Olivia Nuzzi of New York magazine tweeted.

Charlie Spiering, the White House correspondent for Breitbart, was bemused by some of the reactions.

"It's just a meme everybody," he wrote.

Nuzzi responded: "The president sharing a lighthearted depiction of violence towards an entire news network isn't normal, in case anyone forgot."

--CNN's Dan Merica contributed reporting.