In the film, Katharina's angry line to Bianca "[tell] whom thou lovest best" (which William Shakespeare actually wrote and which is grammatically correct) is changed to the grammatically incorrect "whom thou dost lovest best". In his review of the film, critic John Simon caught the error.
When Petruchio asks for Katharina's hand, he makes a globe rotate. But the continents are perfectly drawn on it while the action is clearly set in the 15th century. This is nonsense. The globe looks perfectly contemporary.
When Petruchio arrives on a horse for his wedding, a security guard dressed in black is seen in the background.
Katharina is an unmarried maiden (shrew), yet throughout the movie (most clearly in the early balcony scene) a large diamond solitaire engagement ring is visible on the ring finger of her left hand.