Goof (continuity error): The picture of Pete's wife is different in later episodes than from the pilot. The picture in the pilot is obviously not the actress who plays Pete's wife (Alison Brie) most likely because she was not yet cast.
Goof (continuity error): Office doors and office locations are different in the pilot than in later episodes. Most of the offices in the pilot do not even have names on the outside yet.
Goof (anachronisms): Mad Men is set in the early 1960s; however, in several episodes, telephones are shown with RJ-type modular connectors, which were not introduced until the mid-1970s.
Goof (anachronisms): Episodes from Season 1 to Season 3 feature rotary phones with clear plastic finger wheels. These episodes take place before 1964, when the plastic wheel was introduced. Before that, the finger wheels were black and metal.
Goof (errors in geography): In many outdoor scenes, the tops of palm trees can be seen - Particularly in the horse-riding/stable episodes in the first few seasons.
Goof (anachronisms): IBM Selectric IIs are shown used in the offices. They weren't available until the 1970s. Mad Men takes place in the 60s.
Goof (anachronisms): Secretary shown using an IBM Selectric II typewriter. The Selectric II was introduced in 1971. The show is set in 1960. (In a commentary on the Season One DVD, the show's creator notes that while he is aware of the anachronism and usually quite particular about being period-correct, the typewriter models of the period posed many technical problems for filming, not the least of which was the noise created.)
Goof (factual errors): Lucky Strike was using the phrase "It's Toasted" prior to 1960.
Goof (anachronisms): Wall calendar in doctor's office reads March, 1960 when Peggy goes for a prescription for "contraceptive pills." The first birth control pill was approved by the FDA in May, 1960.
Goof (anachronisms): In March, 1960 Don Draper says "It's not like there's a magic machine that makes identical copies of things." The Xerox copier was introduced in 1959.
Goof (anachronisms): In March, 1960 pitch meeting, Don Draper proposes to client Lucky Strike cigarettes that they adopt the slogan "It's Toasted" (which he supposedly had thought up on the spot). Luckies began using that slogan in 1947.
Goof (anachronisms): This episode takes place in 1960. The railroad station at Ossining is shown decorated with a mark of an "M" on a circle. I presume that this is the mark of the Metro North commuter railroad. But, in 1960, Ossining was on the New York Central railroad.
Goof (anachronisms): IBM Selectric typewriters were introduced July 31, 1962. The Kennedy Nixon election was November. 1960.
Goof (anachronisms): At the end of the first chapter, Draper cames out with a 'new slogan': "It's toasted", but it was really introduced in 1917, not in the 60's.
Goof (continuity error): Upon learning immediately after arriving to work that his boss Don has called in sick, art director Bryan Batt tells Peggy that he's leaving and to not tell anyone. Yet later in the day when Peggy is reprimanded for making spelling errors just before closing time and has to stay to retype a document, Bryan is one of the men that walks past her and looks her over as she warily eyes them.
Goof (anachronisms): Don Draper presents his wife with the gift of a quartz wristwatch. The show is set in the early 1960s yet the quartz wristwatch was not developed until 1967 and the first production models arrived in 1969.
Goof (anachronisms): Character makes reference to the phrase "military-industrial complex" in scene set in March, 1960. This phrase was popularized in President Dwight D. Eisenhower's "farewell address" on January 17, 1961.
Goof (anachronisms): In Spring of 1960, Don Draper makes a reference to banging a shoe on the table. Soviet Premiere Nikita Khrushchev's famous "shoe-banging" incident did not take place until October, 1960.
Goof (anachronisms): In 1960 one of the copy writers mentions the Twilight Zone and imitates Rod Serling saying, "Submitted for your approval." That line was first used on The Twilight Zone (1959) two years later (May 25, 1962).
Goof (errors made by characters, possibly deliberate errors by the filmmakers): While discussing their childhoods, Roger mentions his nanny. He says that his parents got rid of his original, German, nanny after the Lindbergh kidnapping. The Lindbergh kidnapping took place in 1932 with the apprehension of a German suspect taking place in 1934. Since the show is set in 1960 this would make Roger 18 years old at the time of the kidnapping.
Goof (factual errors): In Spring of 1960, Don Draper comes home from work as wife and kids are having supper. Daughter asks if she can go watch Shirley Temple's Storybook. This program only aired on Sundays.
Goof (continuity error): SPOILER: When Betty fires Carla in season 4, Don mentions that she has been the children's nanny since they were born. However, in early episodes, Carla does not appear. The Drapers instead refer to someone named Ethel who sometimes watches the children and does housework.
Goof (continuity error): The exterior of Don Draper's house is first shown at the end of episode 1, season 1. In episode 3, season 1, the exterior of the house is shown again - only it is a completely different house now. The house in the first episode has dormers on the roof and a small portico. The house in the third episode does not have any dormers or a portico. The window size and position are also different.
Goof (factual errors): During the party scene, a radio announcer introduces a opera broadcast of Mozart's Marriage of Figaro as staring Robert Merrill and Joan Sutherland. Neither Robert Merrill or Joan Sutherland included leading roles in Figaro in their repertoire.
Goof (continuity error): When Harry Crane is eating a Stick candy in Pete Campbell's office it's full one minute then half gone then full again.
Goof (errors in geography): Pete & Trudy's new apartment is referred to as being at 83rd Street and Park Avenue, yet the interior shots of the apartment show that it is clearly of post WW2 architecture. All of the residential buildings at that intersection are of pre-WW2 design and construction. (Pre-war apartments were generally considered to be much more desirable, especially along Park Avenue.)
Goof (errors in geography): Pete and Trudy's new apartment is at Park Ave. and 82nd. At the end, Pete looks out the apartment window on a view of Central Park that is impossible from that location. He's looking from the top of the Park, directly south, as though he's on 110th (or higher) between 5th Ave. and 8th Ave. (which encompass the width of the Park). With this impossible view, Pete takes in a nighttime skyline that includes the Chrysler Building and the Empire State Building; this is the New York equivalent of "all windows in Paris look out on the Eiffel Tower."
Goof (errors in geography): When Don agrees to meet Adam in the city at the end, he says he'll be there in "twenty-five minutes". Don is at his home in Ossining when he says this. There is no way he could get to Adam's hotel in Times Square in under an hour, by either train or car.
Goof (continuity error): When Pete and Trudy are in bed together, his hand moves from her hair to her arm from one shot to another.
Goof (anachronisms): Earlier in the episode, the year is mentioned to be 1960. Later in the episode, Joan Halloway uses the phrase "The medium is the message." This phrase was coined by Marshall McLuhan in Understanding Media: The Extensions of Man, published in 1964.