These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: Arguably, Apollo Creed's entrance in his fight against Drago. It starts with an over the top performance that belongs more to a Broadway musical than a boxing ring, has James Brown singing, and has Apollo dressed up as Uncle Sam and dancing. Drago, who is usually The Stoic, is utterly bewildered by this spectacle, and probably qualifies as the Only Sane Man for this scene.
Paulie's robot buddy in Rocky IV. Especially Apollo's reaction to it.
Ensemble Dark Horse: Apollo Creed's nameless trainer in the first film gets an expanded role in all the subsequent ones, including getting a name (Duke). He ends up being the only character/actor other than Stallone and Burt Young to appear in all six films.
Fridge Brilliance: Rocky Balboa works as either a direct sequel to V, a sequel to just Rocky that ignores the four other films, or as a standalone film. One does not need to have any direct knowledge of the prior Rocky films to enjoy it. How awesome is that?
Though he was a former champion in Balboa, so perhaps the third in a trilogy consisting of Rocky, Rocky II, and Rocky Balboa.
Him being a former champion works just as easily as Rocky's backstory. Still no prior knowledge necessary, which is pretty snazzy.
"Funny Aneurysm" Moment: In the MAD spoof of Rocky IV, after Apollo Creed dies, Adrian mentions being nervous because Mickey died in III, and now Apollo, meaning she's next if there's a V. While she doesn't die in V, she does die between then and Balboa.
Hilarious in Hindsight: In Rocky IV, the depiction of the new (at the time) Soviet premiere Mikhail Gorbachev. Probably one of the nicest leaders in Russian history!
It's hard to call Gorbachev "nice" : he was a pure product of the Soviet Communist Party elite, most of his mentors and people who made him Secretary General were leaders of the KGB and the Soviet Army, he was a Magnificent Bastard who efficiently and ruthlessly eliminated (politically, not physically) many of his opponents in the Politburo and his real primary goal was pure Soviet national interest : preserve the USSR's status as a superpower through intense reforms (not that any other leader doesn't do the same). However, it is true that he quickly tried to appear as a nice and wise leader, looking only for peace and such. And this worked extremely well in America and elsewhere in the West (the infamous "Gorbymania"), making his depiction in this movie hilariously stand out.
Not so much for the film itself, but Weird Al's "Eye of the Tiger" parody "Rye or the Kaiser", about a former boxing champ opening a restaurant becomes this when you watch Rocky Balboa.
In the first movie, Rocky walks lil' Marie home. What was one thing he asks her? "Do you have a boyfriend?" Granted, it was in the context of him encouraging her to stick with only good people, but it's funny when you see how Marie and Rocky interact in Rocky Balboa, including her pecking a kiss on the lips.
Although, they don't exactly Get together. Marie, after all, acknowledges Rocky's wife on several occasions, and he appreciates her respecting Adrian.
After completing production for Rocky II, Sly said in an interview "But there'll never be a "Rocky IV." You gotta call a halt.".
Sequelitis: The franchise was widely accused of this, becoming a frequent source of mockery as the series progressed. Averted by Rocky Balboa.
So Bad, It's Good: Rocky IV is often considered as this (in contrast with V, which is just considered bad), what with the over-the-topness, good ol' Cold War patriotism, as well as the antagonist's one-dimensional character and Rocky's narmy speech at the end.
Strawman Has a Point: Rocky IV. Ivan Drago rebels against his Russian handlers and yells that he isn't boxing for Russia, but for himself. Somehow, this makes him a selfish jerk instead of a wordless tool suddenly desiring freedom of choice. Of course, he earlier accidentally killedmurdered a certain former champ, so he can't really gain any sympathy.
Apollo was arguably responsible for his own fate as much as Drago was, given he demanded that Rocky not thrown in the towel for him.
Not to mention the way the movie treats holding the match in Russia. Death threats being made against Drago was treated as an excuse. In real life, it would have been a very valid reason for him to never return to the US.
The death threats are probably treated as a joke because Drago is enormous and surrounded by security. That said, it should be obvious that all the muscles in the world won't save you from a psycho with a gun, especially if you're in hostile territory during the middle of the Cold War.