Is there something that can reveal a non-native speaker?

I like one Russian poet, his name is Joseph Brodsky, who lived half of his life lived in US. And, living there, He mastered in English to the extend extent that he began to write poems started to write poems in it. Even though his work in Russian is granted considered as the most prominent for the second half of twentieth century, his poems (not prose) written in English are also regarded arguably valuable highly and even it is rather strange. Some critics says argued that some lines and figures imagery from his English poems originally written in English sound sometimes are awkward and strange for native English Speakers.  -speaking readers.
I do not know My command of English as well as is not great enough to be able to assess this statements about English Brodsky his English works. No difference for me whether I am reading his English poems or reading the works of Auden or Frost.  when I read his English poems I do not feel that there is something wrong. Just the same feeling of English language as I would read Auden or Frost in the original.

Dear native speakers, what do You think about his poetry? Is there something that you can detect to reveal that it was written by a non-native speaker? If there is, so, please, point them out it for me!!!

Here is one of his last poems written in English.

«TO MY DAUGHTER»  "To My Daughter", Brodsky

Give me another life, and I'll be singing
in Caffé Rafaella. Or simply sitting
there. Or standing there, as furniture in the corner,
in case that life is a bit less generous than the former.

Yet partly because no century from now on will ever manage
without caffeine or jazz. I’ll sustain this damage,
and through my cracks and pores, varnish and dust all over,
observe you, in twenty years, in your full flower.

On the whole, bear in mind that I'll be around. Or rather,
that an inanimate object might be your father,
especially if the objects are older than you, or larger.
So keep an eye on them always, for they no doubt will judge you.

Love those things anyway, encounter or no encounter.
Besides, you may still remember a silhouette, a contour,
while I'll lose even that, along with the other luggage.
Hence, these somewhat wooden lines in our common language.

1994

It is quite impossible to detect a piece of poem is written by a non-native speaker.  This is because poetry has its own set of rules and grammar.  What may be conceived as incorrect English, is perfectly okay in poems.  FOr example, "I love thee not" is considered poetic than "I do not love you."

If you look at the poems of "Mother Goose", or those in "Alice In Wonderland", some are just nonsense and those are written by native speakers of English!  There are times even mispellings are used to convey the images the poet wants make how the readers feel.

There are more clues to detect when a piece is written in prose.  If their command of English is good, it will be impossible to find them.  Usually it is the way in expressing the language in prose that shows traces of the origins of the author.