"A potential for error" is an odd expression, as it suggests there is more than one kind of potential for error. This makes little sense in this context, which is making a general philosophical statement. Perhaps the video goes into more detail about the various kinds of potential for error, but why? I would instead have said:
In any human endeavor there is the potential for various kinds of error
retaining "potential" as an uncountable noun.
Again, it's strange. I'm not going to say that the speaker in the video made a mistake, or is not a native English speaker, but it's possible they are unfamiliar with the typical way this idea is expressed.
In any case, to answer your question: Yes, in this particular use "potential" (meaning "capacity") is a countable noun, but in the same way you can turn any uncountable noun into a countable noun, if you want.
"I like to enjoy a music in the evenings," he said. "Sometimes more than one music, if I'm feeling indulgent."
With creative writing, anything is possible. You just have to be aware the reader might misunderstand what you write, or dismiss it as nonsense.