When Don is looking over Smitty's portfolio, he says "it's got Julian Koenig's fingerprints all over it." Don pronounces Koenig's name as "Kon-ig". In reality legendary ad-man Koenig's name is pronounced "Kane-ig".
Time has elapsed between Season 1 and Season 2 which is established to take place in 1962 so this episode is actually set in February 1962, not February 1961, when A Tour of the White House (1962) aired.
When Don is in the doctor's office at the beginning he had his blood pressure checked. The cuff used had Velcro and in the early 1960s they didn't have that yet.
Near the end of the story, which takes place during February 1962, Don Draper is at home watching The Donna Reed Show. The episode that he's watching is from Season 7, and originally aired 25 February 1965. The Donna Reed Show was only up to Season 4, during February 1962.
When the tow truck arrives to assist Betty, it shows "Kip's Towing and Salvage" Sparta, NY. The Drapers live in Ossining which is almost 300 miles from Sparta.