Uncaught TypeError: c.querySelectorAll is not a function

This GitHub issue tipped me off. It's not related to vue.js nor webpack nor Angular. It's caused by Ghostery.

Turn Ghostery off for your web page and the problem goes away.

In the debugger I can see that c is a variable referencing a comment in the DOM

Well, that's the problem. Comment nodes don't have querySelectorAll. Text nodes don't either. It doesn't make sense for them. Only documents and Element nodes have the query functions.