It's not a transcription error. He said "I don’t want to cast any dispersions."
But enough of that. Let's consider what he was invited to cast aspersions on China about and whether he did, in fact, refrain from.... Or do you want to keep talking about "dispersions"? Maybe you are champing — or chomping — at the bit to defend your President. What are "aspersions" anyway? And it's not as though "dispersions" isn't a word. Is there some requirement that a speaker use the most obvious cliché? Does "cast" demand "aspersions" the way "scantily" demands "clad"? But you can choose to say "scantily dressed" — it's not wrong — so why not say "cast dispersions"?!
To "disperse" is to throw things about, and to "asperse" is to sprinkle things. "Dispersion" is the act of throwing things about, and "aspersion" is the act of sprinkling things about. To "cast" is to throw, so it might look as though we're dealing with a redundancy, but the word "aspersion" also means that which is sprinkled. So to "cast aspersions" is to throw the things that are thrown. But "dispersion" is not defined (in dictionaries that I looked at) as both the throwing of things and the things that are thrown. That's why "casting dispersions" sounds wrong. You're saying throwing the act of throwing.
If I wanted to defend Trump here, I'd try to find a dictionary that gave the necessary other meaning to "dispersion" and, failing that, I'd say that "dispersion" is easily understood to mean, in context, that which is dispersed and, as such, "casting dispersions" makes just as much sense as "casting aspersions," and the people who want to hear the most predictable combinations of words are very boring.
Now, on to the substance. From the transcript of yesterday's Coronavirus Briefing:
Speaker 2: Mr. President, you have said that China is doing everything they can to make sure you don’t get reelected. What specifically are they doing?
Donald Trump: Well, China doesn’t want to see me elected and the reason is that we’re getting billions and billions of dollars, many billions of dollars a month from China. China never gave our country anything. China gave us nothing, not 25 cents. And whether it was Biden in charge of China, which was a joke because they ripped off our country for eight years. And in all fairness to Biden and Obama, this went on long before they got into office. And you can go through many administrations until I came along. Then we signed a trade deal where they’re supposed to buy, and they’ve been buying a lot actually, but that now becomes secondary to what took place with the virus. The virus situation is just not acceptable.
Speaker 2: Do you think that withholding information about the virus is related to them trying to undermine your reelection?
Donald Trump: I don’t want to cast any dispersions. I just will tell you that China would like to see sleepy Joe Biden. They would take this country for a ride like you’ve never seen before.