With a few exceptions (like 28 Days Later which was filmed using standard definition video cameras, and consumer grade ones at that, albeit with professional lenses) most movies use 35mm film which potentially has a much higher resolution than 1080p HDTV/blu-ray. In reality, things like lighting and the choice of film stock can screw this up so they can end up having an effective resolution even lower than standard definition TV. Its not at all uncommon for old films to look very good when transferred to blu-ray, although if the film has been scratched or got dirty or discoloured then a bit of restoration will be required.
I'll have to watch it again, I only remember noticing softness in some scenes, don't remember seeing grain. Some other films from that era that I have on blu-ray show quite a bit of grain. On Total Recall its a fine grain that gives a very pleasing (to me) cinematic effect. On Terminator 2, where it appears in the more darkly lit scenes toward the end, its extremely distracting.