Symptom: after enabling W3TC minify the events calendar month view displays large bullets (responsive mode)
Solution: Yes they will work together even using js minify. Here’s what you need to do:
In the W3TC plugin
1. Under general settings tab go to minify and change from “auto” to “manual” and save
2. Under the minify settings (on the side bar) go to HTML & XML and uncheck Inline JS minification and save.
3. JS Minify can now be enabled. (you do not need to set combine only).
This solution valid as of 9/2/2016 with The Events Calendar/Pro 4.2.5