This post is good.
There are a few basic tips with ochem. It's all about the electrons, so get used to drawing bonds, understanding valence, recognizing differences in electronegativity, and mastering resonance completely. You get these down, and the rest is just variation and application of moving electrons.
Also, there is very little in ochem you have to just memorize, especially with mechanisms. For instance, you may just have to recognize that LDA is a base whenever you see those letters in an equation, but there was almost no mechanism I was given that I just had to take on faith.
It is always a better idea to try to understand how and why the electrons are moving the way they are, even if the professor doesn't say you have to. As the poster above said, all but the easiest of ochem professors are going to give you a problem that requires the application of multiple pieces of knowledge that when memorized will be useless. For instance, you can memorize the addition of alcohols to a benzene ring all you want, but if your professor gives you a benzene ring with a nitro group sitting on it, you had better know how that changes things. Memorizing won't help you here.
Get a head start on diagnosic ochem, which is mass and IR spectroscopy and NMR spectrometry. This seems to be the stuff that maims students worse than anything. You don't need to have it mastered before school starts, but at least have an understanding of what you're going to be looking at. This is not the type of thing you want to try to learn "cold".
If nothing else, don't let anyone else scare you about ochem. It takes work, especially for math people who usually struggle when they realize there are no calculations in almost the whole year. But it's only hard if you spend hours tying to memorize everything instead of just understanding reason for each reaction and using logic to work through each problem. Since the MCAT is going to be testing your ability to apply concepts rather than spew out memorized information, this is going to be better for you in the long run anyway.
Good luck.