Continuity mistake: Don is called to Bert Cooper's office to discuss Hilton coming into the office earlier that day and his (Don's) lack of a contract. Right after Don enters Bert's office, Bert asks, 'when were you going to tell us about this (Hilton)? ' and you can see the contract (with a blue cover) sitting on the table in front of Lane. There are several more shots of Lane and Roger as they discuss the contract, and it is sitting in the same spot on the table. But after Lane explains that Don must sign the contract, he pulls it from his jacket (not the table) and hands it to Don.
Factual error: The show takes place in 1960 and a calendar shows it to be March. At one point, Don Draper chews out Pete Campbell for stealing a discarded health report regarding cigarettes. Don tells him that there is nothing out there that will magically make copies of something (eluding that photocopiers hadn't been invented yet). In 1959, Xerox introduced the Xerox 914, the world's first plain paper photocopier. By the end of 1961, the 914 had generated almost $60 million in revenue. The series takes place in the biggest and best ad agency of New York City. If they didn't own one, surely they would know about the ad campaign surrounding it.
Factual error: When the new secretary is being shown around the office, the cover is slipped off an IBM Selectric typewriter. She is told not to be afraid of the new technology, it was made easy enough for a woman to use. The episode takes place in March 1960 (a calendar is shown) and the IBM Selectric wasn't introduced until 1961.
Factual error: The ad team is trying to come up with a new campaign for Lucky Strike cigarettes, since all health claims must be removed. With a stroke of genius, the slogan "It's toasted" is created and approved. "It's toasted" was the ad campaign that debuted in 1917. In the early 60s, it was "Lucky Strike separates the men from the boys, but not from the girls".
Factual error: During the scene where Don Draper is having an "intimate moment" with Ms. Goldberg on the roof of the Menkens store, crickets are audibly present. Crickets are not present in appreciable numbers on a Manhattan rooftop to produce a sound loud enough to drown out traffic and other ambient noise on 5th Ave. Furthermore, the sound of the crickets is inconsistent with that produced by the native snowy tree cricket. "Crickets chirp at different rates depending on their species and the temperature of their environment. Most species chirp at higher rates the higher the temperature is (approximately 62 chirps a minute at 13°C in one common species; each species has its own rate). The relationship between temperature and the rate of chirping is known as Dolbear's Law. Using this law it is possible to calculate the temperature in Fahrenheit by adding 40 to the number of chirps produced in 14 seconds by the snowy tree cricket common in the United States." (http://en.wikipedia.org/wiki/Cricket_(insect))
Factual error: At various stages of the discussion between Peter Campbell and his wife regarding the purchase of their coop apartment, they discuss down payments and mortgages. Although it may be possible to finance a coop today, in 1960 the buyer would have been expected to pay the total amount up front.
Factual error: In S1E03, "Marriage of Figaro", Don brings home Sally a new dog for her birthday at the end of the episode. Clearly an oversight considering the girth of the wide muzzle and "blockier" forehead of the dog. This presumably leads the informed viewer to surmise that the dog is a British Golden Retriever, a far fetched tale considering the lack of communication between European and American dog breeders during the cold war era. Taking this assumption one step further, the cream colour of the coat is also an indication of a later time period, as the cream colour was only introduced in the past twenty (20) years for British sub-genus.