I don't really know what you should know specifically, but...
I think that the basic VSEPR geometries (linear, trigonal-planar, tetrahedral, ...) would be needed. As for the special names within each basic geometry, you could memorize them or use basic chemistry and determine the shape. Just remember that electron pairs will be in places experience the least amount of repulsion from other electron pairs and bonding electrons. Using that knowledge you can determine how the bonding pairs will be placed and could determine the name.
For Quantum mechanics I would assume that basic quantum numbers should be understood (n, l, ml, and ms). Probably should know Hund's rule and Pauli exclusion principle. I can't imagine that the MCAT will want an in depth knowledge of quantum mechanics, but more of a general understanding which you probably learned in gen chem I.
For solubilities, I believe that there is a general trend and exceptions. I don't really know it off the top of my head, it is easily found in a gen chem book.
For O,M,P directors it is really easy to remember that anything directly attached to the ring that has free electrons will donate (Ortho, Para directors), but its ability to donate decreases as electron withdrawing groups are attached to the oxygen (ie, Phenyl Acetate). Anything with a positive charge is M director (NO2), which can be tricky to see if the structure isn't drawn or you just know it has a positive charge. Any carbon bonded to the ring that is also bonded to an oxygen will be Meta directing. Halides are Ortho, Para directors, but are ring deactivators.
Not really aimless info. Surely the repetition from classes and studying gets it to stick in your brain, just understanding why this or that happens is might be more useful. But then again I love chemistry, so it could just be me.
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