Here's what I think a published campaign adventure should have:
1) Motivation for the characters (and their players) to go on the adventure.
2) A story/plot/background that the GM can convey to the players - and the logical means of sharing that information naturally within the adventure.
3) Clear goals, which are more or less achievable (by sword, spell, or wits) by the character level range indicated by the adventure.
4) A unified theme building up to a satisfying climactic resolution
5) Consistency and logical story/world building.
6) A compelling villain, antagonist ("conflict" to use a literary term)
Of course you need maps, enemies, encounters, treasures, traps, etc. But without the things I mentioned above, you have an adventure site, not a campaign. There are additional items I prefer to see in my adventures, but I think without the above, you're not going to have a successful campaign without adding lots of additional work.
I think these are are extremely important, except 4 isn't always necessary. I've seen pretty great campaigns which didn't have that kind of "theme", just a climactic resolution.
2 also, it doesn't have to be a linear story, but it is a good point there needs to be a logical method to share that information naturally, and I think a lot of adventures screw up here, either by presenting the story solely to the DM, and not giving any way to share it, or providing a ludicrous or extremely boring and video-game-y way to share the story - i.e. a whole bunch of "journal extracts" or the like. This is a pen and paper RPG - just put in an NPC who can talk to the PCs! The DM is right there! The reason video games do that is because writing an NPC who can give information like that is hard, and can get very messy, dialogue-tree-wise. That's not a problem with tabletop games.
5 is something I think a lot of adventures fall down on too. Maybe the majority of WotC adventures I've read from 3E onwards have had some kind of serious logical inconsistency so bad that even when I maybe gloss over it, the players pick it up - and usually you can get them to move on, but it's harmful, and often there are multiple. 4E's initial adventures were an absolute disaster in terms of consistency and logical story/world-building.
5 being done badly is an absolute killer for me. It's one of the few things which will make me look up who wrote an adventure, and basically never buy an adventure written by them again. Not out of anger or whatever, but just like... no. And where 5 is bad, 6 is usually bad too.
Also you gloss over maps, but clear, well-done maps (I don't full colour stuff guys), especially for the DM, are absolutely vital.
Organisation is the other big one. Many published adventures are appallingly badly organised. I very much include WotC and Paizo in this. First off, the story needs a proper, detailed synopsis, so when the DM goes through the adventure, they understand what is going on. Many adventures do not have this, and you're expected to pick up what is going on by reading through the adventure. Which is annoying as hell, and also means that issues with logical inconsistencies are often worse than they need to be, because they're harder to pick up. And the adventure needs to be organised logically, and in a way that's easy to references. I shouldn't have to spend longer taking notes about the adventure, and trying to understand it, than it would take to write my own adventure, but that has literally happened to me, multiple times, from 3E D&D onwards.
For those of you who say "all I want are adventure sites," is that for Adventure Paths and campaign modules that cover levels 1-12 (or 20)? Like, you're really ok with 300-400 page books with no plot, story - just mostly unconnected encounters?
So long as it's entirely clear what I'm getting before I get it, yes.
Personally I don't use published adventures a whole lot, but when I do, I really want to know exactly what I'm getting. There is little worse than buying an campaign boxed set or hardback or whatever, getting it home, opening it up and finding it's the "wrong kind", i.e. it presented itself as this very linear, fully-built-out adventure, but is actually more of a "framework", or a bunch of loosely connected locations. Equally, at least once I bought what looked like a site-based campaign, which seemed to have a massive megadungeon sort of area and loads of small adventures within it, but in fact only detailed one extremely linear path through the whole thing.
One thing I will say is, I buy adventures to use adventures.
I don't buy adventures to read them, and maybe fantasize about running them. I know for a fact that an awful lot of people who buy adventures, particularly for D&D, do the latter a ton, and keep buying adventures even when there's possibility they'll ever get to run them.