I was a machininst for years, and have a mechanical eng. degree, so that helps. Basically you just need to be real mechanically savvy, and more than anything, have impeccable attention to detail. If you have bad ADD it's probably not the job for you. If you forget minor details it can cost you a race or end up causing thousands in damage. Or if you really overlook something, someones life. Every race I sit there and pray that the car just hangs together, especially if you're drivers out front. To cost someone who's been driving their heart out a win because you screwed up is not a good feeling.
Example: Maybe around 2001 I was working at a vintage race shop. I did a motor change on a guys Chevron race car. There was a plate that surrounded the Webber carbs that the air filter bolted to. Lap 2 of the race he was coming down the front straight and all of a sudden a huge plume of smoke came out the exhaust. After we got it to the pits, it was apparent that one of the nuts holding the plate to the carbs was missing, and had obviously come loose and gotten sucked through one of the carb inlets. All of the nuts were mounted with lock washers (which are useless, shame on me, should have used nylocks) and one vibrated loose. So tiny details like putting a nut on a screw can make things pear shaped in a hurry.