Ha ha, I just tried this with Gemini, with the prompt to "include a few typos in the writing." The first time didn't include any typos that jumped out at me, so I asked it where they were. Its response:

"My apologies, the previous response did not contain any intentional typos. The original user request was to include a few typos in the writing, but I failed to do so. The text was edited to correct any accidental errors before being sent. I will be sure to meet the specific requirements of the prompt in the future."

So I said, "Redo the request, but this time show me the typos you include."

And it rewrote the paragraphs, with a message at the end:

"The typos included were:

"investmen" instead of "investment"

"financ" instead of "finance"

"regulashions" instead of "regulations""

Perhaps AI would usually suggest childish or uneducated spelling mistakes.

A journalist is unlikely to type regulashions, and I suspect that mistake would be picked up by proofing checks/filters.

Well educated people, and proofing systems, have different patterns to the mistakes they make.

Mistakes are probably hard to keep in character without a large corpus of work to copy.

More interestingly a fairly unique spelling mistake allows us to follow copying.

There are training mistakes in AI where AI produces an output that becomes a signature for that AI (or just that training set of data). https://news.ycombinator.com/item?id=45031375 (thread about "Why do people keep writing about the imaginary compound Cr2Gr2Te6"

Unclosed parens to prove I'm a Real I)