First of all, thank you all for your comments.  I hadn't anticipated such a negative reaction to an article that was meant to be inspiring to English learners.  The original title of the article was "Change Six Things About Your English and You May Sound Even Better Than a Native Speaker".  The italki editing team changed the title to its current state, and the implication that doing these things correctly will make you sound better than a native speaker is not what I had meant.  However, I still beg to disagree with you all.

Using "good" as an adverb is incorrect English.  I am not criticizing native English speakers, I am just saying if someone wants to learn correct English, then this is the correct grammar to use.  If writing an academic paper or giving a professional speech, using good as an adverb is not likely to go unnoticed.

As for the other five things, my point is simply that, if done incorrectly, a native speaker will notice.  So, if someone is striving to become fluent, then they should pay extra close attention to not making these mistakes.

Furthermore, I do believe it is possible for a non-native speaker to sound better than a native speaker in some regards.  For example, some of my students know (and correctly use) much more advanced vocabulary than many native speakers.  Using this in conjunction with perfect grammar will indeed make the non-native speaker sound better than a native.

The goal of this article is to help and inspire English language learners to fine tune their grammar.  It was not meant as a personal attack on native speakers, and I apologize if it was received that way.