The Rusney Castillo signing deserves mention in the conversation, even if it's just a footnote. It's clearly not of the order of magnitude of many of the moves that have already been mentioned.
But they gave a boatload of cash to a guy whose performance in Cuba had been uneven and who had been hurt for much of his time there. It made no sense when he was signed and was nothing but wishcasting over an athletic looking guy and a desire to be in on the Cuban experience.
And for me, Grady leaving Pedro on the mound after the first bad thing happened in the bottom of the 8th was as dumb as it gets. Hell, sending him out there at all was insanity, but he should have known to remove his starter after any negative result occurred. Critically, Grady should have also known that Pedro was materially worse that year after 100 pitches (Theo's crew had reminded him), Pedro had given up a homer to Giambi in the 7th, the environment at the Toilet was incredibly intense, leaving Pedro spent, and Pedro had sat on the bench after pointing to the heavens while walking off the mound to end the 7th, took off his cleats off and let the adrenaline leave his body. It was screamingly obvious that Grady was begging for disaster with playoff ready Timlin and Williamson in the wings.
If the Sox had not won the title in 2004, Grady's Boner would live in much bigger infamy.