In my current game (I can post a save when I get home) I cannot build West Point, despite having the correct techs and several units of level 6 experience. It's not an issue of already having two national wonders, since it's grayed out in cities where I can still build Globe Theatre. Anyone encountered this?

Edit: I may be confusing experience with promotions. Six promotions on a protective Civ's gunpowder or archery unit do not necessarily mean level 6 experience.

Edit: I may be confusing experience with promotions. Six promotions on a protective Civ's gunpowder or archery unit do not necessarily mean level 6 experience.

That's probably it. Check the levels of your most experienced units (it's displayed in the box at the lower left corner of the screen when the unit is selected). Free promotions don't count as levels, as you already said.