Salkin started his career at Walter Lantz in 1932 aged 19. 

He worked at M-G-M, Universal and Disney, among other studios. He was an animator on the Disney film Lady and the Tramp, and director and animator of Mel Brooks' and Carl Reiner's film The 2,000-Year-old Man. 'Pigs Is Pigs', which Salkin wrote, animated and directed, received an Academy Award nomination for best animated short film. He also wrote an episode of The Addams Family.

He also did newspaper or magazine cartoons, some of which were reprinted in Australia.

Salkin was the visual inspiration for the squinty-eyed cartoon character Mr. Magoo.