While I find this scene rather spectacular as a set piece, I do share some of the reservations expressed.
First the positives. Given the timing of Grond's appearance and the breaking of the gates of Minas Tirith in the film, it would not have made sense to set this scene at the gates. The Trolls and Orcs had already broken through and Gandalf had ordered a retreat to the second level before his encounter with the Witch King takes place. (As an aside, I do wonder why the women and children had not been evacuated to a higher level earlier
.) In terms of the chronology used in the film, therefore, it makes sense for the encounter to take place while Gandalf and Pippin are en route to prevent Denethor's little family bonfire.
It also makes more sense than the book in one respect. It always struck me as rather strange that the Witch King would lead his army into battle on horseback when he had a Fell Beast at his disposal. It seems even more strange that, having confronted Gandalf on horseback, he would then exchange his horse for a Fell Beast halfway through the battle. In this regard, it makes more sense that the Witch King confronts Gandalf while mounted on his Fell Beast and then flies off to encounter Theoden, Eowyn et al on the same steed.
I do also think that, in film terms, it is more spectacular to have the Witch King slowly rise above the battlements for the encounter. The sight of him towering over Gandalf and Pippin on his Fell Beast looks good visually. I also love the shot in which his sword bursts into flames (mirroring, filmically, the text of the book). Although, I suppose this raises the question of why he swapped it for a huge mace/flail thingy in his encounter with Eowyn.
But now for the negatives. As others have said, it rather goes against the spirit of the books that the Witch King is able to get the better of Gandalf. But more problematic, for me, is the fact that it is inconsistent with Gandalf's portrayal elsewhere in the film. It has been pointed out that (while Gandalf the Grey) he was able to defeat a Balrog, and that (as Gandalf the White) he had the better of Saruman. These are the two central villains of the first and second films. Why should the Witch King (who, as has also been pointed out, was driven off by Aragorn in the first film) be able to get the better of him?
I appreciate that the Witch King was set up as the main "baddie" of the final film, and there is a suggestion that his power was enhanced when he assumed leadership of Sauron's Mordor armies (in the scene where he first appears, donning his armour, in Minas Morgul, accompanied by Gandalf's line to Pippin that Sauron had yet to reveal his greatest servant). In film terms, Gandalf's bettering by the Witch King increases the desperation of the battle (if even Gandalf cannot save them), and (as
Essex has pointed out) enhances the accomplishment of Eowyn and Merry. But, to my mind, this doesn't get over the internal inconsistency in "power levels". Jackson could still have had the Witch King breaking Gandalf's staff (which is pretty spectacular, introduces a moment of tension and ties in with his line to Gothmog that he will "break" the wizard), but Gandalf should then have fought back. I would have preferred a "stand off" between them here, as in the book.
And this would also have made more sense of the Witch King's sudden departure with the arrival of the Rohirrim, since I agree that it seems tactically inept for him to forego finishing off his greatest foe if he has him at his mercy.