Movie makers would never get away with putting a 1958 Edsel in a movie set in 1955, but it seems that period movies about musicians are often not nearly as careful.
I was impressed with the guitars used in "A Complete Unknown" but did notice at least one anachronism. The same was true of "Llewyn Davis".
"I Walk The Line" was a little less accurate and the Woody Guthrie film, "Bound For Glory" didn't seem to care.

What anachronisms have you noticed?