1) Torque to spec - Most people don't even understand what this means. Essentially, it means tightening bolts etc. to specifications. This means both making sure they're tight enough and not over-tightened. A bolt that is over-tightened can be just as lethal as one that hasn't been tightened enough. A bolt tightened beyond recommended torque specs can easily break when the vehicle is in use. Torque specs will be different on different parts of the car, and specs will be less for bolts that have oil or lubricant on them than for dry, clean bolts. Your mechanic knows this and has the proper tools, like torque wrenches to make sure everything is done to spec.
2) Computer calibrations - Modern cars are controlled by computers, and these computers are used to make sure everything in the car is functioning properly. When a part is added, tweaked or replaced in your car, in most cases it needs to be calibrated with the car's computer system. Mechanics have the proper software to calibrate parts being added to your car properly. More importantly, they have the training to properly operate the software in conjunction with the car's computer. This is why most mechanics call themselves and each other "techs" as their jobs have evolved so much with technology, they're no longer just basic mechanics.
3) Safety Precautions - Part of a mechanic's training is learning proper safety procedures for different jobs. This has two purposes. The first one is to protect the mechanic's safety at all times. A shop can be a dangerous place, with thousands of things that can kill and maim in the shop on a daily basis. A trained mechanic knows how to navigate the minefield that is the modern automotive service shop. A mechanic also knows what parts of the car can be the most dangerous to work on, so they usually don't have to swallow a pint of oil when changing the oil filter. Mechanics also know how to keep a car safe, so if you don't want your precious BMW 3-Series to end up on its axle in the driveway, you should take it to a professional tech.
4) Offer a Warranty - No matter how competent you are technically, one thing you absolutely can't offer yourself is a warranty on parts and labor. This is arguably one of the best reasons to see a mechanic. If you buy a part and install it yourself and something goes wrong with it a few months down the line, the only thing you'll be able to do is walk to your bathroom, look in the mirror and say "You did a bad job on my car." But if you go to a professional shop and have work done, a reputable shop will offer a warranty on parts and labor, so if you something goes wrong, you don't even need to get upset as you won't have to pay for it twice.
5) Know What To Look For - The most competent professionals in any industry typically have either a combination of education and experience, or just a whole lot of real-world experience. There is no alternative and no short cuts. Mechanics work on thousands of cars in a year and with every job, they learn what to look for, what to do, what not to do and every little idiosyncrasy about a particular make, model, and repair job. A mechanic with enough experience can sometimes even diagnose an engine problem just by listening to it for long enough, while you scour online forums hoping that the person on the other end is actually old enough to drive. Unless you spend every single day around cars and are able to absorb all of the information and experience that a mechanic does after years of work, there is no possible way you'll know what to look for the same way a mechanic does.
OH, AND HAPPY NEW YEAR !!!!