Any water coming into the vessel needs immediate attention. Just a 2-inch hole below the water line allows 79 gallons of water inflow per minute. In a typical 30-foot sailboat, the hull fill up with 2,000 gallons of water in about 30 minutes.
When shaft logs will start leaking, the leak rate will slowly increase – usually due to a loosening packing nut. The shaft log is designed to allow the motor shaft to be lubricated by water as it turns. This means a bit of water will drip into the bilge and that is normal. When the packing nut is too loose, the drip becomes a leak. Tighten the packing nut with engine turned off so that one drip occurs about every 30 seconds.
In case of a broken or cracked hose, just close the seacock, remove the hose and replace with a spare (you do carry spare hoses and clamps, right?). Sometimes, the hose is long enough so that the damaged part can be cut-off and remounted.
A broken through-hull fitting can let in enormous amounts of water and quick action is needed. For safety, keep a properly sized wooden plug attached to each through hull with a hammer nearby to drive the wooden plug into the hole. Some skippers keep all the plugs in a drawer making it more difficult to find the right sized plugs for the particular fitting.
In addition to the wooden plugs, a new product appeared on the market, called TruPlug. It is a tapered circular cone shaped plug made of foam that is a solid, spongy cellular material which is coated with a flexible sealer adding strength and color. I think it is worthwhile to keep one or two of these in the damage control kit since these do not require a hammer, can fit varying size holes and are easier to drive home in hard-to-reach spaces. Here is video on how they work.