Brewing mistakes? I've made a couple of doozies.
1.) 15 years ago, before I knew anything about homebrewing, my wife got into making her own wine, from the juice kits where you get the bag of concentrated juice, you pour it in the bucket, top up with water, pitch yeast, yada yada yada. One day I was with her at the LHBS while she was picking up a couple of wine kits, and I wandered into the "Beer" section. I found a couple cans of Coopers or Muntons or whatever, and decided to give it a try. I boiled it up, poured it into a bucket, topped up with water, pitched the yeast, and then attached the heating belt. Why? Because that's what my wife did with her wine, so I figured that's just what you do when you're fermenting stuff. I wrapped the heating belt around the bucket and plugged it in. Not to a temperature controller. To the wall. For 2 weeks. Banana flavoured nail polish remover. Needless to say, I quit homebrewing for 10 years.
2.) Second-biggest mistake, I'd have to say was the time I brewed a Rauchbier. I ferment in glass carboys, and knowing how dangerous they are, I'm very careful with them. I brew in my garage, which has a rough concrete floor. I knew enough about glass carboys to know that setting them directly on a hard, rough surface like unfinished concrete will cause pressure points that can cause the carboy to crack and break, so I always make sure I set my carboys on something softer, like some scrap lumber or a milk crate. On this day, I grabbed an empty cardboard box from the recycling bin. Picture a desktop computer, on its side, that was roughly the shape and proportions of the box. I set the carboy on top and began racking the chilled wort into it.
I turned my back to clean something and heard a loud "CRASH", and my garage floor was covered with sweet, sticky wort. The box was plenty rigid enough to hold an empty carboy, but as the carboy filled, it got heavier, and sank into the box. Unevenly, as it turned out, causing it to tip over and shatter on my garage floor.
Thankfully, I didn't get hurt, but it drove home the dangers of carboys to me, as the resulting carnage was a deadly mix of big chunks and tiny shards of glass, all razor-sharp. I had to carefully sweep up the glass debris, then pressure wash away the wort lest it attract ants. It was heartbreaking, but I learned a valuable lesson.
Those would probably be my two "greatest hits." Minor ones are more common, like leaving the blowoff tube in the bucket of sanitizer while cold-crashing my beer (hello 1-inch layer of StarSan atop my Octoberfest), forgetting to dump the remaining sanitizer from a carboy before racking wort into it (just a couple of ounces, didn't make a difference), believing that dry yeast requires no aeration whatsoever (at the time, I was siphoning my wort from my kettle to my carboys, which resulted in no froth at all during transfer), and resulting in more banana beer. Also, making a 1-gallon starter for a lager and attempting to pitch it without decanting, forgetting that I should have left room for it in the carboy (5 gallons of beer + frothy foam up to the mouth of the carboy + 1 gallon of starter does not fit in a 6 gallon carboy).