The shot in the opening credits where Mary Tyler Moore throws her hat into the air was shot at the corner of 7th Street and Nicollet Mall in downtown Minneapolis. In May 2002, TV Land erected a statue of her at that spot. The statue faces the opposite direction, however: the buildings that appear in the background of the shot were destroyed by a fire that took out an entire city block on Thanksgiving night in 1982. Many scenes in the opening credits (riding an escalator, window shopping) were shot within a one-block radius of this spot.
The kitten who meows at the end of the closing credits is a parody of the roaring lion which appears at the beginning of MGM films. The kitten's name was "Mimsey"; she was adopted from a local shelter.
In the first season installment "Divorce Isn't Everything", Mary mentions that she can't speak French but can speak Spanish. Later in the series, while at a Mexican restaurant, she indicates that she can't read the menu because she took French in college.
On the newsroom wall there are various world clocks like you would see in a typical newsroom of that era. In the center is the Minneapolis/St. Paul clock, and to its left is a Chicago clock. Minneapolis and Chicago are both in the central time zone, so there is no need to have two different clocks. Furthermore it can be seen that the Chicago clock is set roughly an hour ahead.
Exteriors of Mary's residence show that the apartment with the balcony (which would be Mary's, based on the interior shots of her apartment) is on the top floor, yet Rhoda's apartment is upstairs from Mary's.