Oh man, I have a lot of stories. I suppose this works best as a "lessons learned" because I did learn quite a bit...let's see what I can remember.
Valve open on BK when running off the first wort from the MT...learned early on that I actually need to write "Check Valves" in my brewing steps or I will forget some valve somewhere.
Hop bag tied to the side of the BK with a really long piece of twine. It caught fire and the open hop bag fell in. Learned to cut the twine shorter.
PVC hop spider started to warp and get hot, then fell into the BK. I don't even know how to describe this...the bolts and stuff made it sort-of sag and it gave way. Learned to use a metal collar instead of PVC (the BYO article uses PVC...wonder how long that guy actually used his before writing the article).
Water leaking out of my immersion chiller where the hoses are clamped on. Learned that it's best to either weld barbs to the end, or bend the ends downward (water won't drip upwards).
Got the hoses mixed up my plate chiller. I ended up shooting hot wort into my garden and tap water into my BK. I learned to pay attention, and choose different looking hoses for the wort-side and water-side.
I saw smoke in my front yard when I went outside on brewday. I asked the guy near a truck what he was doing, and he told me that they were pumping this smoke stuff into the sewer system looking for cracks. Not the kind of stuff you want in the air during your brew day. I learned to read the stuff people hang on your door, and not just throw them away.
As other people have mentioned, I've learned to make sure I have enough propane. I find that having two bottles on hand alleviates any problems.
I've done a bunch of smaller things as well...forgotten to add hops, missed the gravity, dropped a glass thermometer too hard into a pot and broke it, boil-overs, left a MT out to clean the next day (holy crap :cross
, made bad recipes, relied on online retailers for stuff to arrive (make yeast starters
after you receive everything), this list could probably go on forever...