Wiktionary
n. 1 (context idiomatic English) insensitivity to and inability to appreciate the elements of performed music or the rhythm, elegance, or nuances of language. 2 (context idiomatic English) Insensitivity to the nuances of current situation or subtleties of a craft; indifference to somebody else's attitudes and moods.
WordNet
n. an inability to distinguish differences in pitch [syn: tone deafness]
insensitivity to the appropriateness or subtlety of language; "he has a tin ear for dialogue"
Usage examples of "tin ear".
He was indifferent to the fact that the French have a tin ear - he was orchestrating for the whole world simultaneously.
And she knew that Granny Weatherwax, whatever her other qualities, had an even bigger tin ear for languages than she did for music.
Even I, with my tin ear, have a sneaking suspicion that this is not great poetry, or even adequate poetry, but (the story continues) a Confederate officer, hearing those distant strains from the defeated army, gave up hope at that moment.