I have finished the Climb Ev'ry Mountain quest. I am suppose to go tell captain gilles and when I do she does not acknowledge my finishing. Did I miss something?
Did it say quest complete?
If so, here's what I found on the Wiki,
Spoiler Even if you've been to the cave on top of the mountain and completed the Quest, you'll get the reward, but, the quest will still be in your Pip-Boy as if you haven't completed it.
Confirmed above with xbox 360 as well. Quest still active, and marker still follows Captain Giles.
So, no you didn't miss anything, it's a bug.