(CNN) Rudy Giuliani just can't seem to get his facts straight.

On Sunday, during one of a series of appearances in which he defended President Donald Trump against the ongoing investigation into Russian interference in the 2016 election, Giuliani was very clear that while a letter of intent had been created regarding Trump's desire to build Trump Tower Moscow, the President himself had never signed it.

In each episode of his weekly YouTube show, Chris Cillizza will delve a little deeper into the surreal world of politics. Click to subscribe!

"It was a real estate project," Giuliani told CNN's Dana Bash on Sunday. "There was a letter of intent to go forward, but no one signed it."

WHOOPS!

Turns out, he had! CNN's Chris Cuomo got his hands on the actual letter of intent -- dated October 28, 2015 -- that had Trump's easily recognizable signature affixed to the bottom.

On Wednesday night, Giuliani admitted he was incorrect about the letter of intent.

"I was wrong if I said it," he told CNN. "I haven't seen the quote, but I probably meant to say there was never a deal, much less a signed one."

If this was an isolated incident, it would still be bad. But it's not even close to an isolated incident for Giuliani. Since becoming the lead spokesman for Trump's legal team back in April, the former mayor of New York City has made any number of misstatements, accidental reveals and other gaffes that have made the water in which Trump finds himself considerably hotter.

Consider:

In May, Giuliani acknowledged -- contra Trump -- that the President had paid back Michael Cohen for the hush payment to ensure the silence of porn star Stormy Daniels. Daniels, who alleges she had an affair with Trump in the mid 2000s, was paid $130,000 by Cohen to keep silent in the run-up to the 2016 election. We later learned that, according to federal prosecutors, Trump directed and coordinated that payment and another to Playboy model Karen McDougal, despite the fact that he has repeatedly denied any knowledge of the payouts.

In June, Giuliani said that first lady Melania Trump "believes her husband" and "knows [Daniels' allegations are] untrue." Asked for comment about that assertion, a spokeswoman for Melania Trump said this: "I don't believe Mrs. Trump has ever discussed her thoughts on anything with Mr. Giuliani."

In August, Giuliani told CNN's Jake Tapper that Trump denied ever having a conversation with then-FBI Director James Comey about former national security adviser Michael Flynn. Except that in July, Giuliani appeared to acknowledge the two men had met -- disputing only whether or not Trump asked Comey to drop the Flynn investigation.

This past Sunday, Giuliani said on ABC that in the answers provided to special counsel Robert Mueller, Trump said that conversations with the Russians about the idea of a Trump Tower Moscow project might have continued through November 2016. "According to the answer that he gave, it would have covered all the way up to November of -- covered all the way up to November 2016," said Giuliani. "Said he had conversations with him -- but the President didn't hide this." Uh, what? One of the things that Cohen had pleaded guilty to is lying about the depth and length of his conversations with Russians involved in the potential Trump Tower Moscow project. Cohen initially said, under oath, that conversations had ceased in January 2016 but had now acknowledged they continued through June 2016. And now Giuliani is floating the possibility that the discussions continued until Trump was elected President?

I mean, come on man!

It's hard to look at that record of botches and biffs and make the case that Giuliani has helped Trump more as it relates to the Russia probe than he has hurt him. And don't forget that Giuliani was initially brought into Trump's legal team because of his past relationship with Mueller -- and the belief that that relationship could bring the investigation to a quick and positive (for Trump) end. That, uh, hasn't happened -- and Giuliani has totally turned on Mueller.

"Wow big crime for a SPECIAL WHATEVER maybe a group of Angry Bitter Hillary Supporters who are justifying themselves by the goal justifies the means," Giuliani texted a Politico reporter recently

So, what is Giuliani's ongoing appeal to Trump?

The most obvious answer is that Giuliani and Trump have known each other for a very long time and Trump thinks that the former mayor is someone on his level (a major political figure) who he can trust to always be loyal. Trump's loyalty is a mercurial thing -- like the rest of him -- and could dissipate or disappear at any moment. Paging Rex Tillerson, Scott Pruitt, Ryan Zinke, Jeff Sessions, Tom Price etc. etc. etc.

Then there is the fact that while he keeps putting his foot in his mouth Giuliani is, in the main, still singing from the Trump songbook: No collusion, witch hunt, Mueller's got nothing. Trump likes when people go on TV and parrot his thinking -- and Giuliani does that, for the most part.

Still, it's hard to imagine that if someone just took the examples of Giuliani contradicting and/or undercutting Trump's Russia story over the past eight months and put it in front of the President, he wouldn't be very annoyed with the damage Giuliani has done.

It's significant -- legally and politically. And it's not going away.