A random, average mook from history is transported to today. How far back could he have been from, and still be able to communicate well?

Hi, assuming you mean he's speaking English, you may be interested in this earlier thread, which has several examples from different time periods and links to a handful of other posts

I am a native English speaker with a hypothetical time machine. How far back in time in England can I go and still communicate intelligibly with the locals?