Commenting each:
Organization: Does the DM have the adventure memorized, papers in order, bookmarks, maps and minis organized, etc
I don't think 5e requires much of this. I use the official adventure paths and I pretty much don't prepare at all, I read it up once it becomes relevant. I can do that easily because I play online. Of course in real life, it might suck for the player having to wait a bit in between, but from my DM-viewpoint I simple enjoy it much more if I explore the world and the dungeons together with the players rather than knowing everything beforehand.
Communication ability: Can the DM communicate the adventure well, and articulate his or her thoughts effectively. Can the DM listen well to different styles of the players themselves
Most important globally. I picked communication mainly because if you talk with your players and figure out what they want and also get them to support you, then you are automatically better at all other tasks.
Letting players run the story: Regardless of what the adventure says, is the DM willing to change all of that if the players want to do things differently. Do the players dictate more of what's going on in the game world. More of a shared story, as opposed to the players only controlling their own PC
I actually hate players that want to derail the story. BUT giving players some DM powers can really help to remove workload off me. So like if a player asks me to describe the area in more detail but the adventure path doesn't specify it in particular I might go say "feel free to tell me and I'll work with that". It often helps to give the surroundings a lot more details without putting all the work on me to think of something and then I use every input I get.
Being a fair referee (objective): Regardless of anything else, is the DM fair and impartial, even if it means things might not go the way the players want.
Honestly if you asked my personal opinion, I'd say "rule strictness" is most important for me. Because DMs house-ruling or not knowing the rules properly is what makes me not want to be a player and is the core reason why I'm a DM and not a player. But I don't think this is globally the most important trait.
Game knowledge: The DM knows all or most of the rules, how things work, and has intimate knowledge of the setting
As said above, knowing the game rules is very important, HOWEVER, I don't think it's the DMs responsibility to know all class feats and stuff out of their head. In fact, I say it's player responsibility to tell the DM what feats apply on their actions. So game knowledge beyond the basic rules is not important.
Storytelling: Does the DM do a great job telling the story. More narrative than the above choice of players telling the story, and the story takes precedence over the dice rolls determining outcome
This is were I suck at and I openly admit to that when recruiting players, but even though I can't do it, I definitely appreciate if a DM can do it well. On the other hand, I'm completely happy with a dungeon crawl. So of average importance.
[World Master/Creativity: The DM runs a really good living world, where NPCs and monsters act and behave like living creatures, often independent of whatever the PCs might have been doing. The world is there to explore, and the PCs have the responsibility to take care. I.e., the DM won't remove the clan of ogres living in the hills just because the level 1 PCs decided to venture up there.
Well, yeah I strictly stick to the adventure paths, so if my players go into a region with monsters way above their level, those monsters are there. But that's not what's important. What's important is that a good DM gives the players some kind of warning or a way to survive. A good DM makes players think it's their own fault that they died (if they do).
Having creatures act realistically even if the PCs are not there is dumb and unimportant. Giving the players the impression of a living world is what's important. Still not too important, though.
Reliability: Does the DM always show up to sessions, and on time?
Very important. Really could be considered the most important thing because if a DM just doesn't show up, he's dead to me and will never see me again. It's an absolute requirement that I expect of every DM and also every player.
Player incorporation: Does the DM make an active effort to incorporate all players into the game equally? Whether it be doing things to allow every PC to shine, or actually engaging players themselves who might not be so forward to contribute because they don't have the stronger personalities of the group
Definitely important, but also a bit player responsibility. And it really is the same a "communication". Players need to involve themselves into the game, if they don't, a good DM will notice and then put that player aside and say "I feel like you're not really enjoying the game much, you hardly participate in the role-playing and the only thing you ever say during combat is >I attack X<. Can I do something to make it more enjoyable for you and get your more involved? Also note that if you don't enjoy the game you don't have to force yourself to stay."
Prone to bribes: Give the DM some food, good things will happen to your PC
Uh... nope. Well, it's important that a DM treats players equal even if he gets bribed.
Adaptability: Unplanned things happen. This DM is good at changing things on the fly and making the adventure continue smoothly
I'm surprised so many people vote for that. I'm not really very adaptable and I don't really want to be either. I want my players to follow the adventure as intended and would go so far and tell them OOC that I rather not want them to do >that<. But HONESTLY, I don't really even run into that problem because I present the players options and secretly manipulate them into doing what I want them to do without them noticing. I also make sure that my players always have multiple things they can do so they don't feel railroaded, but I still have all the options ready and don't need to adapt.
So I'd say adaptability is not important at all.
But I guess differentiating between small scale and large scale adaptability makes sense here. Small scale adaptability for me is if a PC has some cool idea during combat, wants to do an acrobatic stunt, wants to taunt the enemies, wants to hit the eye of his enemy to blind it. Obviously here adaptability is fairly important. Nobody wants a DM who says "That's not in the rules, please do a normal attack or use the help action".
But large scale adaptability in terms of "Let's not go to the dungeon the DM obviously wants us to visit and instead travel from town to town and build a castle with all the gold we accumulated" is where I'd say it's perfectly fine if the DM just says "No" here.
I think people often forget that the DM also should have fun playing, not just the players. Having to make up things on the fly can be exhaustening and not very fun.
Acting: The DM brings life to the NPCs' personalities, and does a great job setting the atmosphere of the adventure
Same as with storytelling, I openly tell when recruiting players that I suck at roleplaying and am way more rule and combat focused, so my players are usually the types of players who can deal with that or even enjoy the rule and combat focus.
I appreciate when other DMs are good at it, but I'm just like "Can you please stop talking to NPCs in town and go to the next dungeon already? I already gave you all information available in the AP!"
Average importance.
I'm kidding of course, I really am curious to see how people view good DM traits lol.
