As I read the sentence, I expected it to turn into something like this:

Inevitably Potemkin and the pro-Austrian party at court planned to take the slightest advantage offered by any carelessness on Paul's part and turn it into a decisive edge.

Perhaps this construction, which I think is fairly common, contributed to the problem in the original sentence.

Interesting. I hadn't thought of that possibility.

"Inevitably Potemkin and the pro-Austrian party at court planned to take the slightest advantage of any carelessness on Paul's part..."

I assumed it was supposed to read

"Inevitably Potemkin and the pro-Austrian party at court planned to take advantage of the slightest carelessness on Paul's part..."

I do agree about negatives often short-circuiting people's brains. I've learned through bitter experience that giving people negative instructions almost never works (very slight exaggeration). With the exception of one word ideas like "NO!" "DON'T" I always try to express instructions positively.
Instead of "Don't send me the copies" (after which the copies were usually sent to me) but "Keep the copies there with you".

Fact, employed by professional interview trainers:
Rule #... Avoid negative sentences. Instead of " I never wrote weekly report" say: "My responsibilities included{...}which prepared me for writing weekly report. I hope I will be given that opportunity in your Company"

On re-reading the offending sentence, I had reconstructed it as Farris did. The author might have avoided the error if he'd simply checked that the words met the intention as inferred by one who would suppose a political enemy would normally want to take more than a slight advantage of his enemy's carelessness.

My initial reinterpretation was "Inevitably Potemkin ... planned to take even the slightest advantage ..."