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.
Big Lipped Alligator Moment: the scene between the princess and her maid, where the princess tried to learn English words, only to snicker when she discovers the words for "foot" and "gown" sound a lot like the French words for "fuck" and "cunt." Not particularly relevant to the plot of the play, and probably only included so that a) Shakespeare could poke fun at the French language and b) Catherine's identity and role would be established rather than just showing up at the very end of the play for Henry to woo.
Crowning Moment of Funny: When Henry begins to try to woo Catherine, she replies with "your Grace shall mock at me; I cannot speak your England." Henry's reaction - "Oh," - is often played for laughs in various productions, as he's clearly thinking 'Oh CRAP.'
Ensemble Darkhorse: The French herald Montjoy, at least for fans of the Branagh production, especially for slashers, since he's the only one who treats Henry with anything resembling respect that isn't related to him or a peasant.
It helps that the actor, Christopher Ravenscroft, was one of the few people from the original stage production Branagh was in that joined the cast of the movie.
Fluellen is a bit like this in some circles — it helps that he's seriously entertaining and deeply earnest about what he does.