Alternate Character Interpretation: 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. The 2012 production at London's Globe Theatre did this particularly well, having Beatrice tear up a little as she spoke about her mother. The same was true for a 1970s production at Stratford-upon-Avon with Judi Dench in the role.
In the Setting UpdateNothing 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.
There are more than a few lines that indicate that Beatrice and Benedick have a romantic history - one that ended badly long before Act I. Beatrice informs the Prince that once, Benedick loaned her his heart, and she gave him hers - but that he won her heart "with false dice." Joss Whedon explicitly starts his film with this idea.
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.
If anything this was Don John's and Boraccio's crossing since they were the ones who planned to frame Hero for this disgraceful act and ruin her life.
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.
It is worth noting that in that era, Claudio was the best she could do after he completely destroyed her reputation. If he'd just recanted there still might have been doubt on her and her family which would have made it difficult to find a good husband (the primary goal of most women in that era), but Claudio marrying her is effectively proof that the accusations were false, restoring her family's good name.
This one really depends on the way the role of Claudio is performed- in the vanilla script he seems to be more mistaken and impulsive 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.