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.
Alternate Character Interpretation: It's very easy to imply, through the body language of the actor (especially in the film adaptation), that Don John is interested in Hero, which actually makes sense, given his actions. In the Shakespeare Retold version, this is explicitly his motivation.
Additionally, it's very easy to interpret Don Pedro as being in love with Beatrice (helped by his proposal in the middle and his melancholy later when she hooks up with Benedick). The 2011 stage adaptation in particular made this clear. The 2014 Vlog 'Nothing Much to Do' also showed this pretty clearly.
It's possibly to show that, underneath her lively personality, Beatrice is sometimes rather a melancholy person. Her "My mother cried" line could have a significant pause after it, implying that she feels guilt and depression for having caused her mother's death in childbirth.
In the Setting Update "Nothing Much to Do," John explains after the scheme takes place that he purely resented Pedro thanks to being Always Someone Better, and he'd intended for Cora to immediately reveal the truth after Claudio's accusation, making Pedro look bad. He deeply regrets that Hero was the one who ended up getting hurt, which allows him to redeem himself just as much as Claudio.
Ethnic Scrappy: A 2011 production of the play by Washington DC's Shakespeare Theater Company set in 1930s Cuba renamed the characters Hugh Oatcake and George Seacole Juan Huevos and Jose Frijoles (Spanish for eggs and beans) before Latino organizations protested (keep in mind the play did not Hispanicize Don John's name into Don Juan). Furthermore, the play featured a Translation Convention where the only actors in the play who spoke with Spanish accented English were those playing the rustics and the servants while the main characters spoke eloquent English.
Idiot Plot: Claudio and Don Pedro already know that John is not a nice guy. And as if that weren't enough, Claudio gets taken in by John's claim that Pedro courted Hero before being disabused of the idea. So, Claudio and Pedro know that John is trying to spread rumors to break Claudio and Hero up - why do they fall for the plot again?
Moral Event Horizon: Arguably, the way Claudio chooses to call out Hero for her "infidelity." He did so loudly, in no uncertain terms, and in a public place. By the standards of the day, Hero's reputation would have been ruined forever, as would be her family's, and a pall of doubt would have been cast over anyone connected to her. Her virtue impugned, she never would have been able to marry; Hero likely would have been forced into a nunnery by her family. No matter how naive he might seem, there's no way Claudio didn't know this when he called her out.
On the other hand carrying on with another man on the eve of your wedding (and Claudio thinks he's seen this with his own eyes) is pretty heinous even by modern standards.
Tear Jerker: Provided the actress playing Beatrice knows what she's doing, and has a Benedick who knows what he's doing, Beatrice's monologue begging Benedick to kill Claudio (or at least challenge him) is virtually guaranteed to leave a sizable portion of the audience close to or actually in tears. The 2011 stage version has an exceptional example.
Values Dissonance: Hero is delighted to eventually get married to the Jerkass who accused her of being a whore on her wedding day. While she was at the altar. In fact, in the BBC's recent setting update of the play in Shakespeare Retold (starring Billie Piper as Hero), she actually doesn't take him back. Same in the recent vlog adaptation, Nothing Much to Do, where Hero forgives him but also doesn't take him back.
This one really depends on the way the role of Claudio is performed- in the vanilla script he seems to be more mistaken than malicious.
The David Tennant/Catherine Tate version (set in the 1980s) has an addition, after the scene at Hero's supposed tomb, where Claudio returns to tomb, gets wildly drunk, and is about to commit suicide, when Hero sees him and steps out of the shadows to stop him. Claudio sees her, thinking (most likely) that he sees a ghost, and passes out. That goes a fair way to making Hero's acceptance of Claudio, even in a modern setting, palatable.
Why Would Anyone Take Him Back?: Branagh did a good deal to avert this by trimming out most of Claudio's more unsavoury lines, giving him a clear view of "Hero" and Borachio, showing his genuine remorse and subsequent atonement, and casting him as a baby-faced Robert Sean Leonard.
Why Would Anyone Take Him Back?: Claudio's unsavoury lines are not trimmed. In his commentary Whedon notes the difficulty of trying to sell the romance in this day and age, and points out that he tried to soften the blow by including a shot of Hero watching the funeral procession, and seeing how torn up he is.
Values Dissonance: Several in moving Shakespeare to the modern day, most notably the plot-driving point of the scandal of a lady not being a virgin on her wedding night (saved in the particular by the extreme of her cheating the night before the wedding). See also Lampshade Hanging above.
Whedon chose not to excise Claudio's line "I'll hold my mind, were she an Ethiope" and instead draw humor from it by having a black woman stand right behind Claudio giving a Death Glare while Benedick watches on with a handless Face Palm.
Tropes from "Nothing Much to Do":
Big Lipped Alligator Moment: One of Benedick's videos ends with him humming My Heart Will Go On over a montage of sloths with no explanation.
Crosses the Line Twice: Verges and Dogberry tackle and kidnap Cora and Robbie, tie them up and attempt to bully them into giving away information. Their methods are extremely incompetent rather than harmful but it is still a pretty horrifying set-up to play as comedy.