A lot of info gets jotted down along the top border for me. ie cpt wounded gets a C. rudder damage a backward sort of tick. You can make up your code as you progress The pics of sails settings can also be used for sail damage by putting a spot on a sail and then striking it out when hit. For intermittent actions like ammo loads, or leaks stopped you can easily rub out the changes with the tip of a baby wipe. I personally never ascribe actions to crew until there are only four crew boxes left and then a bit of work has to be done.
Until that point I assume that petty officers know their jobs and get on with it. Guns must be kept firing, next fire and any leaks, sails and steering last. Permanent steering damage gets a dot in the wheel box and then two if needed, a bit like a cricket score card is done for those who play.

Generally for large games you won't want to be involved in the minutiae of micro managing ships logs. You will be taking an Admiral's overview.
Rob.