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.
Critical Research Failure: A few things in "Ua Hopu". For instance, Interpol having a worldwide tactical team in Osaka, Japan. Which doesn't work since Interpol is a collection of police agencies working together by sharing intelligence. Although Interpol does have a tactical team responsible for protecting Interpol facilities in France.
Same thing with the uniforms of Japanese police officers. Although the basics are correct (e.g. vest, cap, shirt), the shoulder patches and the kanji for the vests are incorrect. In the episode, the kanji is portrayed as "特別警察官", which means "Special police officer" in Japanese. Although it's correct, all Japanese police officers have vests with the kanji "警察庁;", which means "National Police Agency". And don't get me started on the Osaka Police crime scene investigators.
In "A ia la aku" (for the first episode filmed in Hong Kong), the sedan Kono and Adam rode in has mainland Chinese plates, when it's stipulated by Hong Kong laws that mainland-based vehicles should have Hong Kong plates affixed at the front and back in order to be admitted into Hong Kong territory. Also in "Kupuʻeu", the sedan Kono and Adam use is LHD, despite having the correct Hong Kong license plates on.
All of 3.20. There is no chance an Naval Intel Officer (Catherine) has the kind of training to keep up with a SEAL (Steve).
Catherine has apparently been in combat situations previously, as noted during that episode and in season four (she's done three tours in Kabul). Being part of Mission Control probably wasn't her first or only role with the Navy.
Fan-Preferred Couple: Steve/Danny. The sheer amount of fanfiction, communities, and board threads devoted to them are staggering.
"Funny Aneurysm" Moment: Even though this was aired on the same day Amanda Berry was freed after being held captive for a decade, Season 3's "Ho'opio" involved another girl named Amanda being held captive for 10 years. Except it wasn't as happyan ending as the Cleveland case.
Fridge Brilliance: In "Hau'oli La Ho'omoaika'i" (season four's Thanksgiving episode), the plot revolves around a secret service agent that's killed while scouting for the president's upcoming trip to Hawai'i. A random trip to Hawai'i when the president would usually be in D.C. for the holidays seems out of place, until you remember that it's Barack Obama's birthplace. It makes the perfect cover for the real reason why he's meant to be there.
Fridge Logic: In "O ka Pili'Ohana ka 'Oi", why didn't Samantha escape 2 minutes after being left alone? She was locked in a dog cage, which isn't meant to contain humans, who could easily kick one apart from the inside.
He Really Can Act: To the surprise of many viewers, Nick Jonas did a pretty good turn as sociopathic cyber-terrorist Ian Wright in "Akanahe."
He's Just Hiding: What McGarrett suspects is going on with his father's murderer, terrorist Victor Hesse, after shooting him off a cargo ship. He orders the Coast Guard to try to find his body. They haven't, but insist they'll keep looking. 'Course, it turns out McGarrett was justified in his caution.
It has progressed to the point of Ship Tease. Aside from the fact that Steve and Danno are the two male protagonists most likely to Man Hug on a mainstream TV show, in the episode "Mohai" they actually cuddle while watching a movie!
Now in "Ku I Ka Pili Koko", they have officially said "I love you" to each other.
Some of the product placement is among the most blatant on TV. In some instances, it can lead to a Big Lipped Alligator Moment where characters take a few minutes to extoll the virtues of Subway, but other times it occurs during plot-relevant situations.
Paranoia Fuel: Wo Fat has a habit of rigging claymore mines on people's cars, which will detonate once the ignition slot is keyed.
What an Idiot: The Yakuza boss forgets to clear his fingerprints off the stolen Champ box and throws it in the dumpster outside his own bar — leaving just enough clues tying him to the kidnapping that Five-0 can arrest him.
Malia, Chin's ex-fiance. We meet her in He Kane Hewa'ole, and from everything we've heard about her from Kono and what we know about what happened to Chin, it's expected that she's the kind of lady who was willing to dump him after he was disgraced. Instead Malia is a nice lady who loves Chin, was the one dumped for her own protection, and she still wears her wedding ring on a chain around her neck. She tries to be nice to Kono who hates her, and she's so awkward around them both... Poor lady.
Stoic Woobie: Chin takes the fall of his uncle's embezzlement and ends up being disgraced from HPD, disowned by his cop-pride family, and separated with his fiancee. He trades his house's deed for cash to essentially bribe HPD to stop further investigation.
Steve probably counts as an Iron Woobie. His mother dies in a car accident when he's a teenager, and instead of banding together as a family, John McGarrett sends Steve and Mary away to their relatives on the mainland. Steve becomes estranged from his father and his sister (the latter of which probably counts as a Woobie, too), but he grows up to be a strong-willed Determinator without the guidance of his family. And then the series starts, and Steve gets to hear his father's murder over the phone, thousands of miles away and with no way to help. And then Steve discovers that the car accident that killed his mother wasn't an accident, and that his father sent them away to protect the two of them while he searched for answers. And after all of that, it turns out that his mother was alive the whole time, but was in hiding after faking her own death to keep her family safe. Not only that, but she is still keeping secrets, disappears and reappears without notice, and in general is still keeping Steve Locked Out of the Loop. This is on top of all the other crap that gets thrown at him, like having former brother-in-arms betray him, having his former commanding officer and mentor jerk him around, and discovering that his father's friend, the governor, was working with the an who had ordered his parents' executions. Danno often complains that Steve needs professional help, but with a backstory like that, it's honestly a wonder that he didn't turn out worse.