So what the best mistake you've ever made in Skyrim? Mine just happened a couple of minutes ago. Doing my new playthrough, 12 hours in, and then I hear it, that horrible noise, "Do you get to the Cloud District often?". I turn around, equip a AoE fury spell and cast it in the middle of the market, hoping to kill Nazeem with no other deaths. As I'm getting talked to by a guard, all I see in the background is Jon Battle-Born stabbing Nazeem through the clavivcle. After I finish paying off my 200 gold fine, I go to see the damage, and the only people dead are Nazeem, Sigurd, and Lillith Maiden-Loom. Not only did I get who I wanted, I inadvertidly(sic) took out the other two annoying NPCs in Whiterun. My strolls through Whiterun will now be a lot more peaceful.

Going with Hadvar at the start of Unbound. I meant to go with Ralof, but Alduin Fus Ro Dah'd me away from the door and in a panic I ran into the closes door I could find.

Dropping my petty Grand Soul Gem. Picked it up again to find out it "took out the soul". It was now an empty Grand Soul Gem.

Yay! Time for some Mammoth Hunting.

My grip on my controller slipped and I shot wildly off-course with an arrow that would have killed a giant. Ended up killing a Briar-Heart instead.