I think every diver should know:
1. How to plan a dive, including having a rational assessment of gas supply and proposed depths and times, and how that gas supply should be apportioned underwater.
2. How to use depth contours and natural features to get back to the boat, even if the guide is abducted by aliens.
3. How to do basic on-site repairs, like replacing an o-ring or a blown hose.
4. Something about the sea life where they are diving (it really enriches the dive).
5. How to communicate using hand signals, light signals, and written media, and when to use each.
I think every diver should be able to:
1. Go through a dive plan and an effective gear check before diving.
2. Arrest a descent before hitting the bottom, and without disturbing said bottom.
3. Move through a dive site without disturbing anything.
4. Stop, for as long as they want, without hanging onto anything or kneeling or standing on the bottom.
5. Control an ascent, and make stops without hanging onto anything.
6. Maintain situational awareness of depth, time, pressure and buddy whereabouts, even when mildly stressed.
7. Diagnose and effectively manage common malfunctions (leaking hoses or inflators, freeflows, mask fogging or leaking) without losing buoyancy control or situational awareness.
8. Be able to instigate an air-share and execute an air-sharing ascent with good buoyancy control.
9. Be able to deploy a surface marker buoy at depth, and control an ascent while remaining in contact with the line.
10. Be able to orally inflate their BC EASILY on the surface and at depth.
I'm sure I'd add skills if I spent too much time thinking about it, but I think this is a good basic list.