I find that the preview is much better than once the project is rendered. The rendered looks grainy and milky.

Also, when I export a QT movie at full quality there are issues with dissolves. They look like they have bands across them.

Any ideas?

Are you judging any of this on an external monitor or TV connected to the system? You should never judge the quality of your image by what you see on the computer monitor. It isn't showing you what your image truely looks like.