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.
Alternative Character Interpretation: Not a full example as this is actually mused upon in the book, but the idea that the serum doesn't actually transform Jekyll into a different-looking evil man, it simply transforms him into a different-looking man, and it's the intoxication of being able to get away with any crime that leads him to act so evilly.
Of course many adaptations, especially recent ones, decide to eschew the idea that it changes his looks at all and represent the changes purely by acting.
In the book Jekyll pretty much admits that his motive for inventing the serum was nothing other than For the Evulz; he wants to be able to act immorally, but as Jekyll he'll always be worried about his respectable image (not really anything to do with conscience). As Hyde he doesn't have to worry, as the worst people think of him is that Hyde might be blackmailing him (and / or could be his Bastard Bastard son).
Also of more modern debate, about a line Jekyll makes about Hyde growing. The word used there is "stature" which has more than one meaning. Does he mean Hyde would have grown to hulk like proportions or that he's just becoming healthier compared to the much skinnier dwarf form he starts off as compared to the more hearty stocked Jekyll?
And then there's the implied Jekyll/Utterson context as seen below.
Common Knowledge: As noted in the intro, there are many common misconceptions about the novel.
Ho Yay: Too easy to read some Utterson/Jekyll into the former's concern for the latter.
His fears that Hyde was Jekyll's lover, and was using that to blackmail him.
Homosexual undertones were read into the book early on, and a few of Stevenson's gay friends chided him for possibly bringing them to light at all. The recent passing of homosexual legislation up north meant that closeted homosexuality wasn't just a hot-button issue at the time, but that Stevenson could possibly have had it on the mind while writing. A closer look at the edits from the second manuscript seems to support this theory, as Utterson himself starts to read a little bit more into Jekyll and Hyde's perceived relationship. Then again, this was a time when two men could have a completely platonic Romantic Two-Man Friendship and not be chided for it (again, because the idea of two men having sex with each other was just too absurd for Victorian sensibilities).
A short story by Kim Newman, "Further Developments in the Strange Case of Dr. Jekyll and Mr. Hyde", riffs on this; Essentially, Hyde is a separate person. And he's Jekyll's lover.
It Was His Sled: In a big way; the Twist Ending is pretty much the only thing most people will know when asked about this story, even if they've never read the book or watched the adaptations.
Mainstream Obscurity: Just ask a member of the general public to give you even a vague summary of the plot! As mentioned above, most people don't even know that the dual identity was originally a Twist Ending, and it is not uncommon to see parodiesof it where Hyde is literally an ogre monster- rather than simply an evil (but not even particularly ugly) man. To be fair, Hyde is described in the book as a misshapen dwarf so ugly he inspires hatred in people without them even understanding why (possibly an uncanny valley effect due to looking somewhat inhuman).
A lot of people will assume the two girlfriends are part of the book's plot as well; they were introduced in the 1920 silent film (and if you really wanna go back, the very first basis for a lover was in the stage play version) and added to many subsequent versions.
Misaimed Fandom: Many people will use the idea of being a "Jekyll and Hyde" as an excuse for either their own bad behaviour or that of their loved ones: "The real me (Jekyll) would never do such a thing, it was this alien force (Hyde) that took over my body and made me do it." This arguably inverts the moral of Stevenson's story, where Jekyll's refusal to take responsibility for Hyde's actions was a big part of what caused things to go badly.
Moral Event Horizon: Clearly, when Hyde brutally murders Sir Danvers Carew for absolutely no reason, he has reached this point.
Uncanny Valley: This is how the other characters describe Hyde and recognize that he's not quite right. They always describe him as looking "deformed" somehow, despite having no outwardly noticeable disfigurements. This is subtlety is lost on subsequent adaptations, mostly because it's hard to show on screen, and partly because Evil Is Sexy sells better.
Nightmare Fuel: The game has two endings. One of them is reached by simply getting to the church as Jekyll before Hyde. It just shows the church and the word "END" appears while the wedding march plays. A second ending, somewhat hidden, is earned by reaching Level 6 as Jekyll and then proceeding to the end as Hyde. Hyde then fights a boss "demon" at the church, and, upon beating it, turns back into Jekyll. Jekyll's able to reach the church unhindered (all the enemies disappear) and an extended cutscene of the wedding plays. "END" appears when the screen fades out after bride and groom kiss. However, after waiting a while, the music will abruptly stop and the sound effect for the bomb is played. When the bomb "explodes", lightning flashes, the word "END" appears reversed, and Mr. Hype appears as a red silhouette with what appears to be a giant cross embedded into his back. Like everything else about the game, the extended ending is unexplained, leaving it ambiguous (for the wrong reasons) as to whether or not it can be considered a "good" or "bad" ending.
What throws this into Nightmare Fuel is that Hyde's silhouette in the second ending comes out of nowhere, and given what happens to Dr. Jekyll in the book, it can be implied that Hyde still "lives", or worse, that the demon he killed took over the Hyde personality. The lighter explanation is that the cross represents Jekyll finally "ending" Hyde by getting married. This video suggests the latter is a good ending.