Ugh this new schedule has got me all mixed up.
Anyway, CoO has had a couple of abilities that we've seen. It can be used to predict attacks against the user and to sense the presence and vague intentions (aura, basically) of others. For some people, auras take the form of hearing other people's voices, like their souls maybe. I believe CoO can only detect attacks directly towards the user because of the intent behind them. This explains why Enel had trouble against Luffy, because Luffy was attacking the wall and hoping his ricocheting attacks might randomly hit. It explains why Luffy could dodge Hody's water bullets, because Hody aimed them all at Luffy even though he might not be cognizant of their specific trajectories. I believe it also helps explain why Doflamingo's clones are so easily hit by Kyros and later Abdullah and Jeet. In the likely event that Doflamingo has CoO, he probably wasn't able to anticipate the attacks because they weren't aimed at his specific person. Alternatively, he needs to focus Haki on controlling his clones and doesn't have any to spare searching for intruders. In other words, CoO cannot detect objects with no will in them or attacks directed at other people. In general, CoO seems to function as awareness. You can focus on something specific and observe it carefully or be generally aware of your surroundings but lack detail. It's likely that when two CoO users fight they focus on each other and the Haki cancels out, with the better user having a slight edge.
For Armament Haki, we've also seen two basic functions: hardening and countering devil fruits. I like the idea of blackening used as a visual cue but being generally invisible to non-Haki users. Pre-timeskip, CoA hardening was used by the Kujas and probably at Marineford. However, it was invisible because Luffy, and through him the audience, did not use or understand Haki. Post-timeskip Luffy has mastered the basics and now hardening is shown visibly. Oda probably knew he needed a way to indicate hardening but decided to keep us in the dark and wait for a good transition point to introduce it. I think it's been pretty firmly established that CoA doesn't turn things black if it's not hardening them (see Luffy and Caesar).
The main thing I'd like to learn about Haki is how Whitebeard and Shanks cleaved the freaking sky when the clashed back on the Moby Dick. Was that Conqueror's Haki? And if so why did Luffy's and Chinjao's CoC clash look different?