What are the differences between D&D 3.5e and Pathfinder, on the DM’s side?

The very similar question here has answers that focus a lot on the experience of the players.

As a fresh PF DM who was used to 3.5e I’m more interested in changes to rules that I need to pay attention to after I’m already sure that my players know their class and I know the classes of my NPCs. (Unfortunatley this didn’t prevent me from not noticing the stealth errata to unchained rogue’s Sneak Attack but let’s not talk about class features anymore.)

I’m interested in things such as “Acrobatic checks to move past enemies now check against CMD instead of using a fixed DC”, the obvious “combat maneuvers now work really differently” (but that was easiest to spot) and especially any subtle rule change in skill adjudication, resting and mundane healing mechanics.

Basiaclly, things that I’d better know if I want to get the rules right instead of defaulting to the well known 3.5e rule that has been changed without me noticing.

A vague collection (i.e. look at the rules for extingushing a fire) will be enough. I will appreciate answers that provide deeper details but they will not be valued more. I can browse the SRD.

I’m not interested in spells that changed (I will read all spells before using them), skill points being gained differently or in new class features and other things that belong to character building, including the different XP system.

Since the scope of a game like Pathfinder is really vast, I’m asking you to focus on core rules. I won’t bite if you mention some other big or famous changes, but the answers won’t be evaluated on those.