1) It's the only thing that makes the character more human and more worthwhile/interesting (not being able to control his condition properly).
2) It's his only weakness.  If he can control it, he has no weaknesses.  Therefore he is less human in nature and so the audience has less of a frame of reference with him.
3) Was he only pretending to get angry earlier in the film, to intimidate Black Widow?  (When she asks him to come in)
The Hulk is potentially an interesting character if he cannot properly control his condition, it makes him very human in a way.  Most superheroes don't have that much of a problem with their moral compass; they do good, that makes them happy, the world carries on turning (and every superhero being like that gets dull after a while).  On the other hand, some of the most interesting villains in general literature are people who have high positions of responsibility but not "doing good" any more.  Take Hannibal Lecter for example, if he wasn't a psychiatrist, he wouldn't be able to get into Agent Starling's head and scare the crap out of her in the way he did.  The whole scene with her walking into the cell block with the worst cases in for the first time serves up exactly what the audience expects to begin with, deranged serial killers acting crazy, then there's a guy who could pass visibly as a normal person, he's extremely intelligent (either compared to humanity or the average serial killer), and he ought to know better.  The idea for example that a qualified doctor who is about to do an operation on you is actually an absolute nut who is about to do something horrific to you is something that would scare the living crap out of most people.
Real humans are not completely good or completely evil.  One significant challenge in life is determining one's own moral compass alignment (for some people more than others depending on their character to begin with and what opportunities they have come their way in life).  If you throw in a massive advantage over other humans into the equation, balancing up your desires with what kind of person you would like to be suddenly becomes a lot more difficult.  Even if Bruce Banner tries to be very good, when the Hulk comes out he could do unspeakable things and not have his usual control over his actions.  There's the potential guilt of the situation and the constant desire to maintain control (one way or another, one might say one would prefer to control one's self better as the Hulk, another might say avoid becoming the Hulk).
He looked and acted exactly the same on either occasion, in terms of capabilities.  The first time was with slightly more RARGH!  and that was about it.
Then after the interesting point that the Hulk tried to avoid crashing into something that might have hurt people, you know what, there wasn't any danger anyway because he can control himself perfectly well.
Without any weakness, the Hulk was a total plot device.  He was needed to take down those alien wormy transport vehicle things and to provide an element of danger for a while on the ship.  He becomes the Hulk at the crucial second to take down the transport ship, how convenient.
Another question is, would Nick Fury honestly stick Bruce Banner in a situation where he could do as much damage due to lack of control as the aliens are about to do?  If you're playing some sort of strategy game, when would you introduce a unit willingly that can stomp possibly more over your team than the opposing team?  How would you deploy such a unit?  The Hulk is a million times more dangerous than all of the Avengers put together with the lack of control.  With control, he may as well be Superman and Superman really is a dull character.
Having said that, I have Superman Returns on DVD, I quite enjoy it