I think the term "old school" is useful, but it's one of those terms with a huge number of meanings that doesn't hold up well when it's broken down.
To me, as someone who still plays the old rules themselves, "old school" is mainly about two things (no, this is not an edition war point, and yes, this does tie in to actual adventure design): the older rules had actual rules for only a couple of types of situations: combat being the primary area, of course. Later games tend to have rules that cover a broader spectrum of character activity; jumping, intimidating people, etc. That's not a value judgment, just a distinction between the scope of the rules.
So, old school adventure design in one sense is an adventure designed for the smaller scope of rules. In later editions, this probably isn't a desirable feature, because it means you're ignoring several aspects of the game that players have worked hard to prepare for; they have made choices to sacrifice some skills for the ones that the GM is now "writing out of the picture" to work with smaller rules scope. So, writing an old-school style adventure in this respect for a later edition would screw the players in a way they shouldn't be screwed, because it's a bait and switch on decisions they legitimately made in the game system.
Another form of "old school" is the idea of focusing upon challenging the player rather than the character. Again, this folds back into the fact that the older rules "cover" less activity than the later versions. Again, not a value judgment, and again, so people know where I'm coming from, I prefer the old style. Take a skill like "spot." At one end of the spectrum, you've got the 1e method of - if you don't say you're looking, you don't see it. Obviously, that doesn't mean that you don't notice a table, but if one of the legs of the table is shorter than the others, probably the GM isn't going to let the players find it out unless they're doing something that might make the table wobble. In a later edition, this screws a player who chose to max his "spot" skill (ie, the player skill is front-loaded to character creation). I think the more an adventure emphasizes player observations and thinking, the more "old school" it is - but here, there's room for a later edition to legitimately balance the newer and broader rule-set with the older style. The newer rulesets allow numbers to be put on virtually everything, and there is an argument that using the rules well and to their fullest extent would justify or even mandate that virtually everything be rolled rather than determined by the problem-solving abilities of the players at the table. Obviously, no one actually plays this way - the game wouldn't be any fun. But by phrasing it this way, the spectrum becomes apparent. So, to be more "old school" in an adventure that's still fair to players under the new rules would mean finding ways to emphasize skill at the gaming table more than skill at building a character. Giving bonuses to skill checks based on actions, for example.
Now, that's actually how most adventures in the later editions are really done, so this might seem circular. But to make it older school, I think you'd simulate the language required for the "no checks exist" adventure, and then use checks only if the player skill grants access to them. I'll try and illustrate, because I realize I'm not entirely clear:
Current "normal" approach: There is a draft. Any character investigating the source of the draft has a +2 to spot that there is an odd pattern of stones around a vent hole. Further searching has a DC of 14 to find that one of the stones can be pressed inward.
More old-school style of 3e: There is a draft. Characters investigating it will find an odd pattern of stones around a vent shaft, shaped like an eagle in profile. The eye-stone can be pressed inward. Any player specifically examining the stones for such things may make a search check at DC 20. Any character trying to press stones will discover this automatically.
My 3e language may be rusty, but the point is that the "automatic" detection is played down to be much harder, but it's automatic success if the player actually thinks to mess around with stuff and says specifically what he's doing.
It's a pretty broad topic, here..
