Values Dissonance: The comedies in particular work hard to avert this in the adaptation: for example, by having Hero realise her need for independence from controlling men and so refuse to take Claudio back at the end of Much Ado; by having Petruchio become a contented househusband while Kate continues her career in The Taming of the Shrew (essentially a Gender Flip of Kate becoming a meek and compliant wife at the end of the original); and by having the Dream end with the older couple renewing their wedding vows instead of a bunch of twenty-somethings - who've only just sorted out their complex love lives and have only been with their current partners for a couple of days - getting hitched immediately.
The Taming of The Shrew contains the infamous speech by Kate where she says that a woman should view her husband as her lord, and were Petruchio to ask her to she'd put her hands below his feet...and the very next scene reveals that the entire thing was just to troll her sister
Why Would Anyone Take Him Back?: What makes this a unique and modern adaptation of the play is the aversion of this trope. Hero does not accept Claude after her humiliation and finds herself better off alone. It is implied she might be able to forgive him in the future, given that she smiles at him at Beatrice and Benedick's wedding