I really don't mind Tom Bombadil, I even like him, but it's easy to see why he gets deleted from nearly every adaption; it's hard to imagine carrying him off authetically, songs and all, without being annoying. Though I'd almost like to see a director try, just to meet the challenge.
Generally, the elisions and compactings were well thought out. Sad as it was to see the entire Barrows sequence reduce to a bunch of swords being dumped in front of the hobbits, it was a wise choice; in the book it's a chilling sequence and adds in a glimpse of the grief and fall of the great kingdoms of the North, as Tom adds the sense of powers far beyond the little world of the Shire, but it's not necessary. The movie makes the same point subtly and visually with the various ruins they pass and camp among, most powerfully the Argonath.
Glorfindel is one of my favorite minor characters, but he shows up only briefly and it would be downright confusing to have him remain; people not familiar with the books would be expecting this major power to show up again, and of course he doesn't. Giving Arwen his part doesn't turn her into a rival for Eowyn in the warrior maid department. She rides fast and calls upon Rivendell's guardian magic at the Ford, no slaughtering of Nazgul. I expect her brothers will also be elided and she'll take up some of their function as well. It makes her a much more viable and less confusing character for the movie.
More thoughts later -- I've cleverly inveigled a bunch of people to see the movie again tonight and don't want to me late.