Given how often we complain about sequels, reboots, and a general lack of originality in Hollywood, we shouldn't really be surprised that coincidences are used as often as they are, even in great films. And it makes sense -- coincidences are a convenient screenwriting tool. That said, we've reached a point where both Hollywood and audiences unquestioningly accept certain hilariously improbable events. For instance ...
#6. The Hero And The Villain Inexplicably Have The Exact Same Skills
Forget all the father-son mumbo jumbo for a minute, and let's look at the Darth Vader / Luke Skywalker relationship. At the age of nine, Vader was building his own protocol droid, kicking ass in podraces, and well on his way to becoming a(n evil) Jedi. By the time he was in his 20s, he was a highly skilled pilot and up for a potential promotion to Jedi Master. Luke's training, on the other hand, consisted of some vague bullshit from an old man in a mud hut and a few hours with a clearly senile Yoda in a swamp. There is no goddamned reason that Luke should have defeated his father with that kind of training.
And yet he does, because apparently the only way moviegoing audiences can understand good triumphing over evil is if they are competing in the exact same arena, even though this is rarely the case in real life. (Al Capone was arrested for tax evasion, and not all the blackmail, murder, and extortion he masterminded.) Luke should've beaten Vader by rallying subjugated planets to rise up and topple the Empire with sheer numbers, not through a one-on-one sword fight against a lifelong master of the weapon.
To be fair, that mask gives him a -3 in Perception.
Okay, so maybe that could be chalked up to the mysteriousness of the Force and an overly confident Emperor Palpatine. So let's examine The Karate Kid. Danny is, as we've come to learn, a bit of a prick. Rather than do the smart thing and pick up a skill that a) would impress Ali and b) Johnny could never hope to learn, he marches straight into Johnny's dojo and agrees to a challenge in Johnny's sport. Danny should have had his ass handed to him on a silver platter. But instead he got handed a four-pillar trophy, because he inexplicably learned karate and surpassed Johnny's level of skill within the running time of the movie. It probably would've been less of a hassle to simply plant drugs in the evil karate bully's locker, but then the movie would've been called The Plant-Drugs-In-Your-Locker Kid.
"In The Plant-Drugs-In-Your-Locker Kid: Part II, he convinces the bully to apply for his GED, only to ... well, you'll have to find out!"
There's a pattern here across a lot of movies. If the hero fights with swords, the villain will too. If bad guy is going to be a crack shot, so will the good guy. Sometimes, like in Batman Begins, the hero and villain will have similar backgrounds, so it makes a little more sense. Other times, it looks like this:
How is it possible that Sherlock Holmes, a detective, and Moriarty, a professor, have the exact same training in hand-to-hand combat? That'd be like if an interior decorator and a professional snowboarder teamed up to build a military-grade submarine. Nobody seems to be using their exact set of strengths as a character, and instead have to rely on a final battle that involves a skill shoehorned in for them to make things look more badass.
#5. People Only Overhear Conversations When They Are Vitally Important
New Line Cinema
Eavesdropping is the artificial Christmas tree of script writing -- it's easy to set up, it doesn't make a mess, and people have become so accustomed to it that nobody even notices it's fake anymore. Virtually every bathroom scene in every movie ever, important or not, involves someone overhearing a piece of information that changes the course of the movie. Compare that to the amount of times you've ever overheard someone say anything useful whatsoever in a public bathroom. We'll even go a step further and challenge you to name the number of times you've overheard anyone say anything that dictated a future course of action from you. It's probably fewer than three times (all three times in fart Morse code), and almost certainly zero. But we've had entire film series that depend on characters overhearing important pieces of information.
The entire Back To The Future trilogy is held together by a bunch of convenient eavesdropping that occurs in Back To The Future Part II. Jennifer hides in the closet of her future house, overhearing a discussion about a car accident that ruined Marty's music career. Armed with this knowledge, she is able to save Marty from the accident in Back To The Future Part III. Later on, Marty is hiding under a table at the Enchantment Under the Sea Dance, where he overhears Biff's cronies threatening to beat up the Marty on stage, which allows him to spring to action and save his alternate self from a history-destroying ass beating.
"Honestly, Chuck, I have no idea what's happening. This is such a weird school."
Even though he mostly played second fiddle to Frodo through all 42,600 hours of the Lord Of The Rings trilogy, Samwise Gamgee delivered arguably one of the most memorable lines of the series when he denied dropping any eaves. We don't really have much exposure to Sam prior to this scene, so he could have been hoping to overhear a pork pie recipe for all we knew, but Gandalf instead forced him into a months-long journey of eating nothing but elf crackers. Sam, of course, winds up saving the entire world in Return Of The King, which never would have happened had he not been spying on his friend like the neighborhood widow.
#4. Killing The "Big Boss" Automatically Saves The Day
Think for a moment about how every power structure works. For the sake of simplicity, we'll look at McDonald's. If the CEO of McDonald's got arrested for burning down a preschool, every McDonald's franchise in the world wouldn't suddenly implode. They'd simply hire a replacement, issue a public apology, and continue with business as usual. Shit, not even Al Qaeda shuts down when their bigwigs are taken out.
So why is it that when Sauron falls at the end of Return Of The King, all of the other orcs die as well? Or when Tony Stark set off a nuke in outer-goddamn-space, every alien invader on Earth instantly runs out of batteries?
It's a screenwriting trope we're going to call "the mothership", because the most obvious example is Will Smith and Jeff Goldblum destroying the alien mothership in Independence Day, which immediately disables the rest of the alien fleet. We're too lazy to think of a more clever name. It happens when the first two-thirds of a film are spent establishing an enemy that is overwhelming and unstoppable in terms of size and force, and then suddenly realizing that there's no logical way for the heroes to overcome it. So the filmmakers put in a "head vampire" kill switch -- a single target that the heroes can destroy which will send out a shock wave, killing the rest of the enemy force in the process. You may recognize this as a thing that has never, ever occurred -- not once -- in the course of human history. But George Lucas needed a way for Toddler Vader to defeat the entire droid army in Episode I, and that was the only plot idea any of his producers could actually pretend they liked.
"And then this is when Darth Vader says 'Yippee!'"