The Pilot episode, “Smoke Gets in Your Eyes," makes a few minor blunders in terms of technological history. The first time we meet Peggy, Joan introduces her to a typewriter and assures here it’s "simple enough for a woman to use." The typewriter in question is the IBM Selectric II, which was not released until 1971. Indeed the original IBM Seleca wasn’t released until 1961. As this episode was based in 1960, it was an artistic liberty taken by Mad Men, which allowed for technology to magically appear before it was developed.
The audience is once again confronted by the technological limitations of the time when Don claims that there is no "magic machine" that can make identical copies of documents. This is particularly interesting since the first Xerox machine was introduced in 1949. However, these are trivial details that pale in comparison to the overall spectacle that is Mad Men. Let’s draw the line at flying saucers.
Links referenced: TV.com and Wikipedia.