There were things I would like to see added to Bale's performance in the sequels, and perhaps a thing or two I would like to see marginalized, but nothing I would outright remove.
However, these changes are not because I felt Bale's Batman was lacking--quite the opposite. Bale portrayed an excellent version of a young Batman. He was raw, emotional, explosive, and even a little naive--very much like Batman in his first year. However, accepted Batman history shows the Dark Knight going through a character arc that brings him down from the righteous, emotional enforcer we saw in Begins to a very tragic figure that we've seen in comics since the death of Jason Todd, and then (very recently) back to a sort of middle-ground.
It's really a matter of his view of the world. In his early career, as in Begins, he really believes he can save Gotham and vanquish evil. It affects his manner--everything he does is very excited and forceful, because he's pushing towards this goal. Later in his career, though, Batman loses hope. He becomes less naive and begins to realize that his quest will never be complete; evil will always be there. He still does his job, because he knows it to be right--but he knows he can never win.
This worldview gave rise to changes in Batman that were well represented in Keaton's portrayl. He becomes calmer and more collected, because now he's in no hurry. He becomes quiet and methodical and genuinely darker. He's less enthusiastic, he's literally lost all hope.
These elements we saw for the past decade in the comics and in Keaton's portrayl are what I would like to see incorporated into Bale's portrayl. Obviously Batman will always be prone to explosive anger, but I would love to see it hidden behind a calmer, more methodical exterior. The kind of Batman who whispers and stands in the shadows, who strikes with maximum impact but minimum effort. I don't htink seeing this character arc is a pipe-dream; we saw a similar one in Begins. In the film--in the scene on the plane, specifically--Bruce speaks about being Batman as if it will be a limited engagement. He says he will stay in Gotham only as long as he needs to. He believes he can be Batman, save the city, and leave. By the end of the film, this has changed and Bruce knows Gotham is where he belongs, where he will always be. He tells Ra's this very plainly. He knows he'll always be Batman.
What I saw in Begins, even after he put on the mask, was the gradual birth of Batman. Aside from the character arc I just mentioned, there is another subplot about Bruce's motivations--Bruce slowly comes to learn that he can't be Batman for himself. This attitude is finally reflected when he says to Gordon that he needs no thanks. Indeed, the true Batman is not seen till the very end of the film, where appropriately the title is finally shown; Batman has just then begun.
So, following from this I expect equally significant progress in Batman II. Specifrically, to the darker, tragic Batman I spoke of above.
After this stage, Batman in the comics has recently come back from this slump. We also saw this stage in The Dark Knight Returns, where Batman's hope is somewhat revived and he returns with a new zeal for his mission. This stage I would like to see in the third film.
It's a maturing process. In Begins we saw the young, enthusiastic Batman. In Batman II, I'll be looking for the reserved Batman, and in the third a middle ground, the final, mature Batman who has come to know that hope is a necessary component to his mission. I think the death of Rachel would effectively begin stage 2, but I haven't given much thought to what might begins stage 3. Robin, perhaps--of course, Robin would only exist in a support capacity (survelliance, computer and detectve work) rather than as a real sidekick. He would, of course, have to be no younger than sixteen and no older than seventeen. I think Robin COULD work, but only if used very carefully. It might be safer to avoid him entirely, but I think it would be unfortunate to miss him.