In my first year of brewing, I have had the good fortune of making some really big mistakes and suffering the consequences. Now I don't do those things any more and I am a better brewer for having found out the hard way:
Don't use a glass hydrometer to push out the paper towel stuck in your beer thief.
Get into good habits and keep them. Clean and organize thoroughly and often!
Don't be "pretty sure" that valve is shut before you starting filling, MAKE SURE it is shut.
Make sure to treat yourself to a beer as a reward for your work. Beer begets beer.
Make or use a checklist and time sheet every time you brew. You might have it down pat when everything is cool, but if a variable throws a wrench in your process you will be able to look back at what step you're on without missing a beat.
For the sake of domestic harmony, get good at cleaning up after your brew day. Eventually, somebody will notice and say "thank you".
Make room for brewing. Even if you have to share space with a kitchen, laundry room or garage, give yourself enough elbow room for you and the gear you need. Don't stumble, trip or reach over things while you are trying to be productive and efficient.
Don't ever, EVER,
EVER turn your back on a boiling pot, flask or beaker on the stove!
Value your mistakes and don't let them discourage you. There is more to brewing than just making beer. Many have spent their lives brewing in search of spiritual wisdom. Let the beer teach you.
It is less probable that man invented beer and more likely that beer created man.