Typically, the most frequent points of significant water intrusion while underway, that is less or non-existent when not running, is shaft(s), rudder posts, and open seams (on woodies), particularly in the forward hull. Other potential sources would be raw water systems for engine(s), genset, refrigeration & A/C, and washdown systems.
I like to use Polyseamseal to seal the open seams as it tools easily with a wet finger, is white, completely paintable, a bit flexible and long lasting. We had to make this repair in Mexico when the seams opened up and we did it while in the water, from the dock and from a dinghy. Very effective, both functionally and aesthetically.
An easy way to ventilate the lower hull or bilge areas is to provide for air movement between all compartments from stem to stern and install some 6" muffin fans in the stern area, perhaps venting through the existing transom vents, and let those run when shorepower or genset ACV is available, either automatic or via a switch. The muffin fans can be either 102 VAC or 12 VDC. They are quiet and long lasting as well as inexpensive. And yes, it is worthwhile, at least IMHO.