Here's my two cents:
1) Finally researching Optics and upgrading a Galley in your coastal city. Loading all of your good units in it to go attack the barbarians in Terra, then finding out that Alexander's culture totally envelops your port and he JUST cancelled Open Borders with you! I felt so dumb...
2) Acting like Civ3 and forgetting all about cottages. Then finding out that Washington just researched Liberalism and you're still going for Compass!
3) Setting a galley or something to "explore" and then forgetting about it until another one of your galleys runs into it.
4) Leaving all of your military units in other people's territory and then wondering where all your money's gone. That 'Away Cost' is pretty clever.
5) NOT switching civics because you're in a Golden Age...then finally realizing your mistake when one of your cities celebrates "We Love the Despot Day"

.
6) Playing on Always War and No City Razing, then going to take over the AI like there's no tomorrow. In the end, there really isn't...because you're getting -4 gold on 0% research. Okay, this wasn't me, it was my brother, but still...
7) Saying, "Oooh, let's see what's in that area" only to find you can't go in there because that's Alexander's territory. That thin blue line is hard to see.
8) Saving a GP for a golden age and then forgetting about him until you get another...of the same type.
I've actually encountered all of these, except #6.