As with the question of why does Katherina succumb to Petruchio, the question as to whether or not the play is misogynistic has been around for hundreds of years. In the film, which, as we have seen is essentially the same as the play (excepting the very end), the story of Petruchio's taming of Katherina against her will is very much treated comically, presented as a story where the obstinacy of the woman and the resoluteness of the man work to offset each other a la the irresistible force meeting the immovable object. However, the fundamental fact is that a woman is forced to marry a man against her will simply because her father is offering a large dowry. Petruchio even admits that money is the main incentive in his search for a wife, and from the time he meets Katherina to the time the play ends, he never shows any real affection for her, or expresses anything which seems like genuine emotion. His few speeches are all about lying and subterfuge, often mixed with hunting metaphors (in which Katherina is the wild hawk that needs to be trained). These speeches imply that there is no affection in him whatsoever for Katherina, nor any guilt or remorse as to the situation he is forced her to go through. Furthermore, the end of the play is treated very much like a celebration and Petruchio very much like a conquering hero; his taming has been successful.
One of the main criticisms that has been levelled at the play is that by presenting such a situation, with Petruchio very much in the role of protagonist, and also treating it comically, the play is in fact championing the subjugation of women, and celebrating patriarchy and societal male dominance. As such, the play is often seen as Shakespeare's most openly sexist piece, with its main purpose being to cater for the predominately male audience who would have been attending his plays in the late 1590s. Needless to say, many productions and adaptations of the play have thus steered away from this implication, instead offering some sort of counterweight to the apparent sexism (see here and here for more information on the various productions and adaptations of the play), and this film is no different. As explained above, the film includes a final scene not in the play, where Katherina gets the last laugh on Petruchio, thus removing the sense of patriarchal dominance, and instead replacing it with a sense of masculine gullibility.
Whatever the case regarding actual productions however, some critics argue that the play is not sexist at all, even without the addition of new material, and is instead mocking male notions of superiority and celebrating the resiliency of women. Much of the debate is tied into Katherina's final speech, and whether or not she is being sincere. In this adaptation, as explained above, she clearly isn't in any way sincere at all, but there is no indication in the text one way or the other to indicate how Shakespeare himself regarded the speech (although in the play, she does willingly leave the banquet with Petruchio). Actresses usually play the role either devoutly sincere (such as in the BBC Shakespeare version) or heavily ironic (such as in the 1929 adaptation, where Katherina winks at the assemblage behind Petruchio's back). If played sincere, the implication is that Petruchio has simply worn down Katherina, tired her out to the point where she is simply unable, or unwilling, to resist him. In this sense, then, it is difficult to argue that the play is not at least in some degree misogynistic. On the other hand, if the speech is played ironically, the reverse is true, the play becomes a mockery of patriarchy and a celebration of feminine wiles.
In terms of this particular adaptation, according to Franco Zeffirelli's autobiography, he and Richard Burton both wanted Elizabeth Taylor to deliver the speech ironically, but Taylor felt it would be better to speak completely seriously, and then undermine that seriousness by leaving the banquet without Petruchio, thus subverting his apparent authority over her and showing that he hasn't tamed her at all.
See here for a discussion of the apparent misogyny in the play in general, and the final speech in specific.