Award Snub: Gavin MacLeod (Murray Slaughter) was the only actor to have never been nominated for an Emmy (Georgia Engel never won either, even though all six of the other regulars did, but she was nominated), but (unusually for this trope) MacLeod is almost universally considered the weak link in the cast (and, along with Betty White, is one of only two actors on the show who is generally remembered for another role - in his case, Captain Merrill Stubing on The Love Boat.)
Oddly enough, the show itself seems to make a comment on this. The show's final Teddy Awards (shown in Season 7's "Murray Can't Lose") chronicles some of Murray's frustrations with never managing to receive a win for his work, while the rest of his colleagues are often acknowledged. In the episode itself, Lou hears from an inside source that Murray is apparently a lock to win that year, and Murray becomes excited by the prospect of some recognition. However, Murray ends up losing, left out once again (while Mary, Lou, Sue Ann and Ted all managed to win that very night). In the end, Murray's wife tells him to read out what would have been his acceptance speech, and it results in a Crowning Moment of Heartwarming when everyone finds out that the speech was going to highlight the depths to which he loved all of his friends.
Dueling Shows: For some reason, MTM often gets mixed up with That Girl by modern audiences. Technically not an example, as the former wasn't created until after the latter had ended its run.
This might have been caused by Nick @ Nite and TV Land when, pre Network Decay, Nick used MTM as the icon for its lineup of classic well-known shows, while TV Land used That Girl to symbolize its lineup of lesser-known shows.
Fair for Its Day: The season 3 episode "My Brother's Keeper" has Phyllis discovering that her visiting brother (who she'd first tried to fix up with Mary and then suspected of being romantically interested in Rhoda) is gay. Her reaction? Relief that he won't be having a relationship with Rhoda. It's likely the first TV episode in which a character is unambiguously happy to find out a relative is gay.
Growing the Beard: The first two seasons had a lot of episodes focusing on Mary's dating life. Starting in the third season, the writers shifted more of the focus to the Work Com aspects and engaged in more Character Development, including allowing Rhoda to get some self-esteem and making Ted a more rounded character.
Reaffirmed in its history with the Emmys. While it would always manage to do well with the Academy in its years on the air (a rarity for any TV show running 7 seasons), it would only be its last 3 seasons that would win it the the top award for Outstanding Comedy Series.
Harsher in Hindsight: In the series finale, Ted is thrilled to find he'll be the sole team member staying at the station. Not only was Ted Knight the first cast member to die in 1986, but it took more than 30 years for the second with Mary Tyler Moore's death in 2017.
Glen and Les Charles also wrote an episode. Both also served as co-creators and co-executive producers of Cheers.
Seinfeld Is Unfunny: The show was so influential and widely imitated that younger viewers might wonder just what the big deal is.
In particular, the show's whole premise (a single 30-something year old woman who was more focused on having a fulfilling career than landing a husband) was seen as being very progressive for its time. As, until then, women on television were usually portrayed as "the nagging housewife" or given some other male-dependent role. Today, with single, career-driven women being very common in media (and in Real Life thanks to further advances in Feminism), the whole idea seems rather quaint.
The early episodes got a lot of comic mileage out of the then-novel idea that a newscaster, such a respected figure on TV, is actually an idiot who just reads what the producers give him. This has become such a common joke since then, including in James L. Brooks's own The Simpsons and Broadcast News, that the novelty has worn off.
During the episode where Murray wants to have another child and his wife doesn't, he asks everybody's advice on how to handle it. Ted suggests putting something in her drink as a last resort. Back in The '70s, the reaction to this suggestion may have been "Oh my God, what an idiot," but in the present day when we've come to learn just how serious Date Rape is, the reaction is more likely to be "OH MY GOD, WHAT THE FUCK IS WRONG WITH YOU?!"
Nowadays, Lou Grant's frequent commenting on women's backsides—including Mary, his employee—and open sexism would've gotten him fired. Possibly the worst example of this happens in the episode "Who's In Charge Here?" Lou is getting promoted to program director and needs to decide who should replace him as producer of the news. The logical choice would be Mary, the associate producer, but Lou instead gives the job to Murray, a news writer with no management experience. When Mary asks him if he passed her over because she was a woman, he matter-of-factly tells her that of course he did.
What an Idiot: Used often in-universe with Ted. A key example is Season 6's "Once I Had a Secret Love", where he undergoes a search to find out who Sue Ann slept with the night before and is unable to notice the obvious clues leading to Lou, even after WATCHING HER KISS LOU RIGHT IN FRONT OF HIM.
Ted: Sue Ann wore your overcoat, she brought your socks, she just kissed you tenderly on the head. (Beat) You know something, Lou? If her new boyfriend finds out, she's going to kill you.