Just a quick note to myself, and others who could face this same problem:
When using Vue inside py4web, as it's done in the todo application included with the code, using the vue devtools tab in the browser does not work out of the box.
This is the message the extension shows:
To solve it, adding
Vue.config.devtools = true;
to the beginning of the file static/js/utils.js allows you to use the vue devtools to debug the vue app. It's a good idea to remove this line when the app is sent to production.