Always watch the footage all the way through before coloring. Then your looks will fit & change with the mood of the film. You’ll also be able to grade faster since you know what’s coming up & will already know the problem shots/scenes.
Knowing all of the footage is crucial. Start grading without knowing what the content is and you have no clue how to make the grade enhance the mood of each scene. You might grade the first scene too dark, just because it looks “cool,” or you might get to a crucial mood change a scene early. Watching the whole piece also helps to identify the problem areas ahead of time. Knowing which areas will give you trouble will help you pick your “hero” shot faster in the balancing/primaries stage, and you’ll have an idea of how aggressive you can make your look without causing problems. You’ll also be able to observe the production design and get an idea of what look might bring out the best of the colors already in the shot.
Knowing the footage ahead of time will make your actual grading session go much faster. The client may think you’re wasting his time and money at first by not starting right away, but once he knows how much faster you’ll be able to grade (and with fewer mistakes, hangups, and re-grading), he might just change his mind.