While entering text, I was forced into an amused frustration by typing the word statistic followed by two apostrophes for a quotation mark, followed by a period. The result: statistic became the letter M.

Example: m''.

What might the mechanism behind that be? Something mathematical perhaps?

'm'm...I think it is the keyboard going quickly from symbols/numeric to alphabet. The letter m in the alpha keyboard occupies the same key in the symbol/numeric keyboard. I was able to replicate the 'm phenomena you describe. If you press the single quote mark key very slowly it would produce the 'm all the time. But then why press the single quote key when you have the double quote key right next to it?

They key I was hitting was the comma. If you hit the comma and swipe upward, it enters an apostrophe. Do it twice and it creates a proper quotation mark and saves you from having to enter the symbols keyboard.