Hmm, I'm guessing "depth of understanding" is accomplished by most people, so I'll describe my approach to "ability to avoid mistakes." But as I haven't discussed this facet with other people, my process won't be optimal as it's based solely on my own limited ideas.
I did all my practice exams in timed conditions, and after each one, I painstakenly analysed the errors I made and devised heuristics (methods of doing problems) to avoid these errors in the future. This analysis composed a 17,000 word document. Furthermore I devised an exam procedure - I established a mental frame beforehand which I adopted whilst undertaking the exam, determined precisely how I would use reading time, and exacted a sequence of actions to perform whilst completing each question. In short, I tried to "perfect" my technique as TT puts it.
In the end I'm not sure whether my efforts paid off, the one mistake I made that cost me a 50 wasn't something I had come across in my analysis, it wasn't even in my "Compilation of Tricky Points," it was simply a matter of interpreting a question too hurriedly.