I can often tell an upper intermediate or advanced student by their one-word reply to a simple question. If I ask a student if they speak English and the reply is "yes" then perhaps their English is quite good but more often than not it is at a lower level. If their answer is "yeah" then I know their English level is quite high.
As far as producing the so-called Teacher Speak or Teacher Talk, I learned to do this long before becoming a language teacher. Living and working in foreign language environments, I was unable to learn all the languages of the countries I was in. But I, at least, learned how to simplify my English by employing all the methods that Keith Folse described so that my listeners who spoke a bit of English could understand.
I speak slower and more distinctly. I use simpler vocabulary and shorter and simpler sentences. I avoid idioms. I try to keep the concepts simpler.
I have learned how to listen to myself speak and even to pre-listen. I can put myself into my listeners position and listen to what I am saying or am about to say. Not only trying to keep it simple but also constantly questioning myself if there is any way my listener can misunderstand me.
Often the contraction "can't" can be confused with "can" by low-intermediate students. So I will try to say "CAN-NOT" making a clear distinction between the two syllables.
Although I am speaking slow, my mind is working fast testing different words and phrases, looking for alternative and simpler ways to express a point.
My students recognize right away I am using a Teacher Talk with them. Low-level students are happily surprised that they feel they can understand everything or nearly everything I say. Upper-level students are annoyed and feel my speaking is not challenging enough. When teaching mixed level classes I have to remember to try to do both at different times.
A related problem is the language of textbooks. On occasion I come across books written for low or mid-intermediate students with advanced English not only in the examples but in the instructions to students.