Fair for Its Day: There were no main cast members of color on the show, but, particularly in later seasons, there were several African-American guest actors, in roles that were treated with total respect. "That's My Boy?" not only presents an affluent middle-class black couple, but ends by revealing that Richie goes to school with the couple's kid (and in fact the African-American boy gets better grades than Richie) — a somewhat risky line at a time when integrated schools were still controversial.
In the episode "Romance, Roses and Rye Bread", Sally finds herself dealing with the unwanted affections of Bert, who works at the deli where the gang regularly gets lunch. While several moments would be a bit more uncomfortable in today's world (such as when Burt shows up at her house uninvited), they were a bit more socially acceptable at the time, and the resolution of the story resonates today: no matter how much of a Dogged Nice Guy Bert was, and even if she was actively seeking non-Bert suitors, Bert was wrong to pursue her to such lengths, and Sally did not owe Bert anything more than a "not happening".
In "My Husband Is Not a Drunk", Rob becomes a Hypno Fool, with a bell making him act like a falling-down drunk. In 1974, Dick Van Dyke publicly admitted to having had a serious drinking problem for the preceding 25 years.
In "The Sam Pomerantz Scandals", a comedian friend of Rob's does an impression of Jimmy Cagney as John F. Kennedy including the line: "You dirty rat! You're the guy that gave it to my brother, Bobby!" This, of course, was long before Bobby Kennedy was shot for real.
Getting Crap Past the Radar: In the episode "There's No Sale Like Wholesale", Rob goes to a friend of Buddy's to get a fur coat for Laura. After he gets there and picks out the style, he realizes he doesn't know the size. A janitor, who is a man with a small frame, walks by, and Rob asks him if he'd put on the coat. The guy gets a funny look on his face and says, "Are you in show business?" Rob replies yes, and the janitor says, "Look, I don't go for that!" and hurries off. Later, Rob has the coat on himself to look at it in the mirror, and the janitor walks past again and sees this. He asks Rob, "Does your mother know you do this?"
In the episode "Brother, Can You Spare $2500?", a pawn shop owner suggests to Rob that a show about a pawn shop owner would be a hit. How right he would be.
In the episode "Go Tell the Birds and the Bees," Richie asks Rob whether a fox and a rabbit could fall in love. Rob says no, but come 2016 and lo and behold...
Mondegreen: In the "Head of the Family" pilot, the Alan Brady character was originally named Alan Sturdy. This was changed for the series because it sounds like "Alan's Dirty".
Nightmare Fuel: The final shot of Rob's nightmare in "It May Look Like a Walnut", with him being cornered by the crazed-eyed Laura, Mel, and Buddy (who possibly are actually aliens/transformed), is surprisingly freaky.
Not So Crazy Anymore: in the episode The Plots Thicken, Rob is flabbergasted while talking to a funeral home on the phone. After he gets off, he tells Laura, "How do you like that?! They have a layaway plan. You pay now, and go later." Nowadays, many people prepay for their "final expenses" without a second thought.
Dale McRaven co-wrote nine episodes. McRaven is best known as creator, executive producer, and executive consultant of Perfect Strangers and as co-creator, producer, and supervising producer of Mork & Mindy.
Norm Liebmann and Ed Haas wrote two episodes. Both are best known for developing The Munsters.
Howard Morris directed five episodes and guest starred in "The Masterpiece". The same year, he began his recurring guest role on The Andy Griffith Show as rockthrowing hick Ernest T. Bass (and lent his voice to many cartoon characters).
James Komack directed 2 episodes. Komack is best known as creator and executive producer of Chico and the Man.
Theodore J. Flicker also directed 2 episodes. Flicker is best known for co-creating Barney Miller.
Laura seems like a fairly normal housewife now, but at the time it was apparently a big deal that she was regularly shown wearing pants. Amusingly, Lucille Ball, who along with her then-husband, Desi Arnaz, owned the studio facilities where The Dick Van Dyke Show was filmed, had previously worn capris on her own show, I Love Lucy.
The level of sexual tension between Rob and Laura was also pretty daring at the time, though the image has now been completely eclipsed by their separate beds.
In the fourth episode, Sally starts crying the day after a date where again her aggressive sense of humor and Brutal Honesty scared off her date.
In the episode "Where You Been, Fassbinder?", Sally is humiliated when the old high school flame she thinks is there for a dinner date turns out to only be there to sell insurance. Although later in the episode, things get sorted out and he was hoping for a date, but he overheard Sally talking about a made up boyfriend.
Unfortunate Implications: In the first-season episode "The Bad Old Days", Rob and Buddy rant about "The decline of the American Male." Then Rob has a bizarre Dream Sequence in which he abusively treats Laura and Richie like a feudal lord, through which he is ultimately persuaded that it is wrong for men to treat their wives like servants... because too much housework makes women unattractive. Seriously, that's the Aesop. By general consensus (including the cast and crew) this is the worst episode of the series.
One episode had the Petries set Sally and Laura's cousin up with the same guy, and consequently Rob and Laura get frustrated when he doesn't commit to either of them. Then, in a conversation with the man over coffee, he reveals that he's been married three times before, two of those times with the same woman — this utterly stuns them. Although the man doesn't seem to think it's a big deal, he goes on to admit that he divorced those women (and tends not to date in general) because he has a bad temper and tends to, specifically, "hit people he loves" when angry. Not only is the fact that he's been married before treated as almost equally bad as his tendency to hit his wives, but the show has the man come off as an oddball for not thinking it strange. Laura and Rob then joke about him after he leaves (although specifically joking about his phrasing, that he "hits people he loves".)
Shame over previous marriages also forms the basis of the fairly serious episode "Divorce" where Buddy believes Pickles is cheating on him because she's too ashamed to tell him that the man she's sending money to is a former husband, who's blackmailing her with the threat of revealing their past marriage (albeit part of her shame also came from the fact that said former husband was a "jailbird.")
The many episodes where it's presented as a perfectly normal idea that every woman should be a House Wife can sit a little oddly to present-day sensibilities.
Though the show as a whole Zig-Zagged the sexist Stay in the Kitchen trope, some episodes especially in early seasons played it perfectly straight (such as "Washington and the Bunny," "To Tell or not to Tell," and "The Bad Old Days"). While the cast realized "Bad Old Days" went over the line even at the time, "stay in the kitchen" was still very much an ideal for much of America and the women's revolution was only just gaining traction.
The episode where Sally is set up with a guy, and Rob complains about the society rule that men are intimidated by funny women, is at the same time dated and relevant to this day, as a commentary on male competitiveness.
There's an episode where Ritchie has been getting beat up on by a girl at school, but won't fight back because she's a girl. While this particular bit of values dissonance really depends on the person (some people still hold to it to this day and some don't), the reveal that she's punching him (in the throat on one occasion) because he refuses to kiss her when she demands it likely wouldn't be treated like the cute little misunderstanding that it was back then in the show.