So in AVID my blacks and whites look perfect, but when I render and watch the footage in quicktime, they are not as sharp and washed out. What is going on?
You are seeing the difference between digital television standard of 16-235RGB and the computer range in quicktime as 0-255 which allows for 0-16 more for blacks and 235-255 for whites.
Try exporting out with RGB selected in QT settings first.