Ember should be used more often. It saves a ton of time with large apps and has really neat plugins like FastBoot. It's underrated.

I think the pendulum will keep swinging between the minimalists (React/Vue.js) and the frameworks (Ember/Angular).

Ember is completely underrated and overshadowed by React right now. It takes some of the best ideas from React (components, shadow DOM, FastBoot) and puts them in a cohesive framework that has an incredible support ecosystem and upgrade path.

That was my impression too.

So React showed that Angular and Ember shouldn't be used, but Vue is just shinier than React right now?

No one gets fired for using React. Vue isn't even shinier in my opinion. It makes the same templating mistakes that Angular and Backbone did.

What are those mistakes? I don't do front-end development so my knowledge is very limited with these (I know the names and a basic idea what they do)

To me, it's the reintroduction of custom templating. I appreciate E4X/JSX syntax because it's just a thin layer of sugar which is compiled to regular JS syntax. It also lacks custom implementations of loops etc, requiring the user to write _Javascript_ not some non-standard templating language.