Although the movie takes place in 1959, in one scene near the end where Francis and Dale are walking along the East River in New York, one can clearly see the twin World Trade Center towers in the background. These towers were not completed until the '70's.
The recording studio is wildly anachronistic. The sort of console in the control room didn't exist until at least the mid 70's. They were much smaller and simpler in 1959, when stereo was in it infancy.