Some people I've heard coming back from recent theatrical screenings related that the puppet looks far better than on home media releases, where apparently there were more than a few issues of colour loss, resulting in a more obvious 'green' look over the puppet. Makes me think that perhaps, for most shots, a simple colour correction could suffice to make the puppet more properly blended within the environments.
For some other shots (see: the Alien escaping the trap, the Alien running towards the shutting door) the problem is entirely compositing wise i.e. how it interacts with the environment