Gloria's hair during the breakfast scene is neatly groomed in close-up but much less so in wide angle shots.
When Sam is consoling Gloria in front of the mirror, Gloria's reflection drops her right arm down. When the real Gloria (not the reflection) turns away from Sam, her right hand can still be seen tucked in the crook of her left elbow.
At a meeting early on, someone references Eisenhower as President of the United States, when in fact it was John F Kennedy who had held the office at that time.
While VCR's did exist in 1961, they cost tens of thousands of dollars and were found in television stations, not individuals' homes. The first consumer VCR was introduced in 1963 and they didn't become commonplace until the early 1970s. Gloria should have had some reaction to Sam mentioning them.
As Sam is getting out of the bubble bath he can be seen wearing either a speedo or underwear.
Al claims that Gloria Collins will commit suicide on October 16, 1961. However, this is the leap date and Gloria does not attempt suicide until two days later.
This episode begins on October 16, 1961. In an early scene, Sam mentions that Roger Maris is about to break Babe Ruth's home run record. Maris, in fact, hit his record-breaking 61st home run over two weeks earlier on October 1, 1961.