When Betty is complaining to Francine about the family photos in her kitchen, Francine hands her one photo that she tells her is nice. Betty is holding the photo with two hands (you can see both sets of pink fingernails on the sides of the photo) but when the shot cuts to Betty, she is holding the photo with her left hand only and has her right hand holding up a cigarette.
When Pete and Trudy are in bed together, his hand moves from her hair to her arm from one shot to another.
Peggy gives Don a bundle of mail along with the envelope from Adam, and one of the other letters is marked "Via Air Mail." The return address is from another business in New York. Air mail is used for mail traveling long distances such as cross country or internationally, not for mail moving within the same city. Also, the envelope has a four cent stamp, which was the cost of regular first-class postage in 1960. Air mail was seven cents.
An envelope on Charley Fiddich's desk has the USPS "full eagle" seal, designed to help usher in the independent United States Postal Service. The USPS did not come into existence until July 1, 1971. (It was previously called the United States Post Office Department.)
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.