What punctuation issue do people come to blows over most often? Single versus double quotation marks? How to use an ellipsis? Dashes? Apostrophes?

Nah, it's commas. Specifically, the serial comma. (Some people call it the Oxford comma. I don't particularly like Oxford so will stick to the proper name of a serial comma. Though as a peripatetic writer, I am aware of other punctuation elements tied to real places, such as the River Piddle Slash and the Shitterton Dash.)

A serial comma is where a comma is added before the final conjunction in a list, usually "and".

Example without a serial comma: Karl wrote Turner, They Move Below and Harvest Festival.
Example with a serial comma: Karl wrote Turner, They Move Below, and Harvest Festival.

Generally, individuals either brandish knives and shout "You must always use a serial comma!" or they raise a club and yell "You must never use a serial comma!" Yep, it's all or nothing for most people.

But guys, come on, peace and love! Chill! In most cases the answer is not to be found at one extreme or the other. Those who say it should never be used are being silly. Look at this sentence.

The inspiration for "Fast Times" was my ex-lovers, Siouxsie and the Banshees and The Teletubbies.

Wow, how many ex-lovers did I have? It becomes a lot clearer (and prevents me being taken to court for slander) if I add a comma:

The inspiration for "Fast Times" was my ex-lovers, Siouxsie and the Banshees, and The Teletubbies.

Phew! They were just inspirations, and separate from my ex-lovers.

My infinitely wise view: if the comma clarifies things (prevents confusion), I definitely add it. If it creates confusion, I definitely leave it out. In all other cases it doesn't matter one way or the other as long as you're consistent. That's how all punctuation should be used - the minimum to achieve clear communication.

And clarity of communication is always the issue. This week a court case hinged on a serial comma. If a certain dairy had used one they would have won the case. As it was, they lost. Hard cheese.