Changes that you weren't bothered by.

[Essex]

re Boromir (and other people's simillar points):

The Nazgul saw Frodo had the ring in Osgiliath, so why the heck would Sauron all of a suddenly think a different hobbit had the Ring in Rohan?

Jackson himself says they borroweed this scene from the ROTK part where Frodo feels impelled to hand over the Ring to the Witch King near Minas Morgul.

A few reasons why Sauron (in the movie version) did not find out about the Ring at Osgiliath.

1/ Did the Witch King actually 'see' the Ring?

2/ Was it actually the Witch King anyway? (which leads me to my final point)

3/ If it wasn't, remember Faramir shot his Winged Beast, so we can surmise that the beast may have been dealt a fatal blow and the Nazgul was left without a ride, having to make it back to Mordor 'on foot' and been out of action as he was earlier on at the Fords of Bruinen.