My worst mistake ever was right at pitching time, when I knocked over a White Labs yeast vial (yeah, no starter for this brew) and poured it all out onto my countertop.
Hmm. No other yeast in the house. Saturday evening, so LHBS is closed until Monday. Do I leave my wort sitting around for two days? Nah...
I can't remember when I last cleaned the countertop, but at least judging by a quick eyeball check all I can see is a bunch of breadcrumbs. So I scrape up as much of the spilled yeast as I can (using the side of a knife to slide it onto a thin sheet of metal), then go ahead and pitch it.
I lost so much yeast in the process, I underpitched by a ridiculous amount, and I guarantee I picked up some wild nasties from the breadcrumbs.
But the brew turned out fine. A little slow to start, but it was done fermenting within a week, and came out perfectly clear and clean with no off flavors.
Most of my other mistakes have been failing to follow recipes correctly:
My first brew ever, I picked a recipe that called for honey malt. "What's that?" I asked the friendly supplier in my LHBS. "Oh, that just means regular honey. 'Malt' is used as a generic term for any kind of fermentable stuff" he replies. So in goes a pound of honey. Later on I learn that he was completely wrong, and honey malt is of course a kind of specialty malt. But in retrospect this was actually a good thing, since real honey malt wouldn't have worked for me as I didn't know how to mash it. I also later found a different LHBS with more knowledgeable staff
Another time I was doing a partial mash using first wort hopping. But I forgot I was first wort hopping, and for some reason decided to recirculate a huge amount of wort back through my grain bed by pouring it back out of the brew kettle into the mash tun (this was only my second partial mash, so I hadn't quite got my technique down). Of course this ended up with all my hops mixed in with the grain. Inexplicably, it didn't occur to me that I needed to get them back into the kettle, so I ended up with almost no hopping at all. This was an English brown with half a pound of molasses. After 3+3 weeks in primary and bottle, it was so bland as to be undrinkable: overly sweet, but lacking any kind of flavor whatsoever. So I left it and moved onto the next brew. A year later, it tasted great. Still a little on the sweet side, but it developed a wonderful complexity, with a kind of raisiny liquorice character that must have originated with the molasses.