Corrected entry: In the flashback scene at the fur store, Roger hands Don his business card. Don sees Roger's profession and says "Look at that, can I give you a call?" Roger replies "No, I want you to call me at that number for specific delivery instructions." The business card was the device for Roger to communicate to Don his profession (a necessary plot advancement), but Roger certainly would have given Don delivery instructions then and there, rather than have Don call the office (where Roger's secretary would answer) for instructions to deliver a fur box for his mistress. (00:07:10)
Corrected entry: Ken Cosgrove asks Jane if she would like to go to a Mets game at Shea Stadium. The episode was set in 1962 and Shea Stadium didn't open til 1964. The Mets originally played at the Polo Grounds.
Correction: Ken says "I have tickets for the Mets tonight. Great seats for, probably, a terrible game. I'll be by at five." There is no mention of Shea.
Smoke Gets in Your Eyes - S1-E1
Corrected entry: 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.
Correction: In that episode Don was being sarcastic when he said that. He was making the point that he has the same info that Pete does, and if he thought it was useful he would have used it to begin with.
Corrected entry: The daughter of Don (green eyes) and Betty (blue eyes) Draper has brown eyes, a genetic impossibility.
Correction: Not true. High school biology over-simplifies genetics to: The brown gene is dominant over the blue gene. But in reality the genetic determination of eye color is much more complicated. While it's not especially common, two blue-eyed (or green-eyed) parents CAN produce a brown-eyed child.
Correction: He didn't have the specific delivery instructions when he bought the coat because he didn't yet know when and where he'd be meeting Joan to present her with it. The very next scene is the two of them meeting discreetly in a hotel room. Roger likely hadn't booked this yet (or even more likely this is the sort of thing he would entrust to his secretary and he would have no clue about the details) so couldn't tell Don there and then. He's obviously not going to have the fur coat delivered to his home address (where his wife lives). If the writers had wanted, then Roger could have had the fur coat delivered at work, then he would have to give those details to Don, and Don would still cotton on to who and how he important Roger was.
It's more likely that Joan took care of reserving a hotel room, told Roger where and when, and then he told his secretary that some fur guy would be phoning asking for delivery instructions for a mink coat, and that's where he should deliver it. This way Roger is free to make up an excuse such as it's for a potential client to give to his wife etc. and nobody at the office is any the wiser to Roger and Joan's affair.