I think most people have covered this but vavet touched on it more specifically. First, establish a methodology that works so everything is done the same way. Any experienced pro that cares about their work will do this. Not only does it prevent mistakes and callbacks, it saves time. You can work faster by making less mistakes. But don't make working fast your goal, your goal right now should be eliminating mistakes. Some of these ideas come about from looking at your work and acknowledging the things you can screw up or forget. Some come from experience, but hopefully you only need to learn a lesson once.
Where and how you lay out parts you removed. The ground is generally bad if you're walking around. One errant step and parts go flying. But maybe identifying an area you won't need to stand/walk would work. Or better, have a rolling cart nearby to place the parts in the order you removed them.
Orienting bolts so they go back in the correct location and sequence. Put them with part you removed or on the car in the location they belong (new part can't go in without removing and reinstalling the bolts). Make sure there is no way for 10 bolts to come out and 9 bolts to go back in. Put them all in an obvious location not obscured by other tools, rags, etc. while you're reassembling.
Where you place tools while you're working. Under the hood, I use the left and right edges or the cowl. Never in the middle where I'll slam the hood shut and see the impression of the wrench on my hood. The last thing you do before you close the hood, check the oil cap, scan the left and right fenders and the cowl, no tools...good to go.
Leaving reminders for yourself so you can't proceed or wrap up a job without tripping over that reminder. I'll throw a quart of oil on my engine if I get distracted after I've drained the oil. I'm not closing that hood with the quart staring at me. If the drain bolt hasn't been put back, it's sitting on top of my new oil filter. When the filter goes in, so does the drain bolt. I know I won't miss a shiny new filter on the ground, but the drain bolt is far easier to miss.
Once you come up with that methodology, don't deviate. As you get experience, you might add to the methodology, but following those steps saves you from making mistakes.
But as vavet mentions, you'll get distracted, there will always be a reason to deviate (just keep it to a minimum or if it's outside your control, find a new place to work). Realize THAT'S when the mistake is going to happen, when you altered the routine. If in that moment you recognize that you're doing something different, leave a reminder for yourself. For example, if you didn't clean the rust off a hub/rotor yet and get called away before you could install the wheel. Thread the wheel bolts/nuts on the hub. The wheel isn't going back on with those bolts in the way, you'll remember then.
Finally, it's been mentioned here, but rust messes with everything. Fasteners and mating surfaces are particularly susceptible to creating problems. Clean off the parts before you reassemble and it will spare you headaches later. A couple years ago I learned that the hard way. My car was 12 years old. Previous to this I haven't kept a car much more than half of that. I always torque the wheels properly after I install them and I never miss a bolt and always check each bolt twice. A couple wheels after the winter wheel changeover, I discovered the bolts were backing out. That's the first time that's ever happened on me. I retorqued them and checked a week later and they were backing out again. I pulled all the bolts and cleaned the threads, put them back in and noticed the bolts were seating much more smoothly right to final torque. And a week after that I rechecked the bolts, no change, they were snug. Lesson learned, just clean the crud before you put it back together.
