Well, there is a lot of the dirty humor and snarky contemporary commentary which doesn't translate well. But the humor can come through with a little tweaking of of acting and setting.

Many years ago now I saw a Stratford production of The Taming of the Shrew. Bianca was played as a blonde bimbo, complete with Marilyn Monroe white dress and hairstyle, and the funniest scene had her tied to a chair while Kate started pulling the legs off her favourite teddy bear, each limb removal accompanied by a dismayed shriek from Bianca.