I actually have a couple of good ones:
Personal: We had a big beefy ATX power supply that we had bought to test some high-current motors. We calculated that, for the worst test case, we might need 100A, so we got a Corsair with one single 100A 12v rail.
Trying to make a clean job of breaking out the wires, I took everything apart and wired up a terminal block screwed into the outside of the case such that, with no leads screwed in, you could install the PSU into a computer and use it as normal. Problem was, the inside was packed tighter than a duck's butt. Some fine engineering in that thing, for sure.
So somehow, one of the screws I was using to fix the terminal block to the case went in a bit too far and shorted the case to the +12v rail. Of course, the outputs are all floating so that was fine, ish. The problem came when I was trying to track down some noise in our linear regulator. I hooked a scope up to +- 12v (ground to negative), and I'm sure you can guess what came next. Connecting ground to the -12v line (currently 12v below building ground) created a loop through the chassis of the scope.
Of course, the power supply had no problem driving a half ohm load at 12v. For about half a second we wondered why the lead sparked when we connected it. Then the 22 gauge test lead caught fire.
Took a while to figure out where the short was, but after cutting the bolts flush to the required length, everything worked just dandy. Didn't damage any equipment either, only dignity.
Work: We made an LDPC error corrector. Everything was going great, so we spun version two with some tweaks. Got it back a few weeks later, had the test guy wire it up in the lab and it just wouldn't correct anything. The part worked fine for any checkable metric - configuration worked fine, power wasn't a problem, every electrical check was great but it just output nonsense. it took about 4 weeks before someone finally figured out that nobody told the test guy that version two used a new parity check matrix. The code generation software was totally incorrect for the part.