White balancing is key to any video shoot, but more so for underwater due to the constantly changing degree of light on the reef or wreck. There are several white cards you can bring down with you (even a slate will do in a pinch).
Another thing to remember is you can't always use a red filter. Red filters are good in "blue water" conditions, but not so good in the "green water" conditions we get from time to time here in Florida. I have both a Red (blue water) and a Pink (green water) filter for just that reason and I carry them both with me on each dive.
That being said, filtering is not the cure all, but rather filtering
attempts to restore color and sometimes a small increase in visibility. Filtering
helps, but it's not perfect. Proper lighting is also key and in conditions of low viz, I usually concentrate on wide-angle closeups and wait for the next time when the viz is better.
I agree with the others that shooting to "fix in post" is not the best way to go about it, but there are times when you can't avoid it. I have fixed a few video pieces here and there in post when I thought I had done everything correctly during the shoot.
Hope these tidbits helped. You can reach me anytime via email:
doug@videodudeproductions.com if you have any other questions I may be able to help you with.