I think there are three essential alterations in Year One--which I call mistakes--that either Denny O'Neil missed or approved of:
1. Alfred is already Bruce's butler.
2. Gordon comes to Gotham from somewhere else--instead of having been a cop in Gotham for a long time.
3. Gordon doesn't have a daughter.
There might be others, but my brain isn't coming up with any at the moment. I didn't really care for any of these "mistakes" in the story.
Others say that Pennyworth being the butler early on is an improvement--well, it does give Bruce someone to talk to. So for expository reasons, Alfred plays that part that Bill Finger brought in Robin to play. On the downside, it gives Bruce a kindly father-figure to raise him--which ought to mute the sense of tragedy in Bruce's life. It makes more sense that Bruce had a horrible childhood after his parents death and thus was never able to come to terms with his loss, remaining stunted in his emotional development. If he has Alfred in his corner, it's hard to figure out why Bruce is so cranky--especially in the O'Neil edited comics that followed Year One, which is the cranky pants era of Batman.
As far as where Gordon comes from--it works for the particular story that Miller is telling in Year One--but in a larger sense not much is gained. Most other tellings of the Batman origin have returned to the old state of affairs. In BATMAN BEGINS, Gordon is already a beat cop in Gotham when the Waynes are murdered. And in GOTHAM, he's the homicide detective working their case.
The omission of Barbara as Gordon's biological daughter is the worst mistake. I realize that Denny O'Neil hated the character--and probably Miller did, too. But if they were going to write Barbara out, then she should have been left out completely. Yet O'Neil keeps her in Batman continuity--so she can later be shot by the Joker. I sometimes wonder about the psychology of these writers and editors who take their frustrations out on these fictional creations by having violence done to them (Keith Giffen was the same way with characters he didn't like). Keeping Barbara in continuity requires a big stupid explanation to explain how she can be Gordon's daughter yet not his daugher in Year One. Why couldn't she just be away at a private school--if Miller didn't want to use her in Year One?