Knowledge is the most important item to have onboard any dive boat. Not only the Capt. / Owner but ALL divers onboard should have at least basic knowledge of what do in the event of a diving related emergency.
The USCG offers safe boating classes (which reduces the owners insurance costs). Additionally I would not dive unless someone (other than myself) onboard was trained a least through Rescue Diver. A"non-diving" surface support person will not be of much help if they don't know how to respond in the event of an emergency.
That being said, I realize that you were really looking for an equipment list specific to diving. As a charter boat Capt. myself here are a couple things that often go overlooked - trying to repeat items already mentioned above...
1. Emergency Action Plan -- before every trip you should (as a group) go over what to do when it all goes wrong - know where the closest chamber/hospital/USCG Station is, have a recall signal, a lost diver plan, and a communication plan.
2. At least 2 anchors, you will never regret having a backup anchor when the first one gets stuck or lost.
3. VHF radio AND everyone onboard should know how to use it to contact the USCG or other boats in the area on channel 16 -- a 60 second pre-dive brief will suffice.
4. Good sturdy dive ladder.
5. And last but not least, a complete list of emergency contact information for each diver on board.