Big spoilers if you haven't read chapter 860.
My biggest thing about this chapter is this.. HOW THE HELL IS DOGTOOTH THIS STRONG? Whitebeard never showed any form of advanced haki in the war of the best (that we know of) so how can the strongest man in the world and his crew not show any form of greater haki, when big mom has a commander that has observation haki so great that he can see into the future? This puts a whole new outlook on everything. Maybe shanks appearing at marineford out of nowhere was some form of haki. Who knows. Nothings certain anymore. So here are my thoughts, I'd like to hear yours.
Next level observation haki let's people see into the future like 5 or 10 seconds. This gives an explanation for how Rayleigh can block kizarus kicks at LIGHTSPEED, because I highly doubt he moved that fast. I think his haki is just better, and it now gives everybody with observation haki the possibility to keep up with the fastest people in one piece. If they train enoigh.
Next level armament haki. Now we haven't gotten an example of this for sure, but I think that maybe the reason big mom's skin is so tough is because she has trained her armament haki to the point where her skin itself is constantly in a state of protection. This could also be an explanation of why kaido can't die, and is "immortal". The only thing that bothers me is that Whitebeard showed no such type of ability, and I feel like he should have had it, being the strongest. Maybe it was just because he was old and sick, or maybe I'm completely wrong and advanced armament haki is something completely different.
KINGS HAKI. The only thing I can think of is when shanks comes onto whitebeards ship and is using his haki constantly while he is walking, we haven't seen anybody use it like that, and he even cracks the ship with it. Which is ridiculous, and we dont even know for surr thats what it is. So does the next level of kings haki even do? Or do we even get one?