Improvement

A friend of mine has a theory.

Each language is a mountain and its difficult part is their pike.

The pike in German language is at the beginning, because you can not go ahead if you are not able to conjugate everything correctly, or you will see your self yourself speaking like Master Yoda, and it's not good at all.

Now, I face the English pike: you have already learnt learned the rules, but can not avoid making some mistakes. You can already speak and understand without any big problems, but you can not say that you're Fluent fluent and still having some problems in a formal conversation or in a movie, in which Characthers the characters speak very fast or in a dialect.

My question is: How can you improve your English at this level?
Is reading and speaking are enough? What kind of grammar stuff should I look for?