In Three Things to Unlearn from School, Ben Casnocha cites Bill Bullard's list of three bad habits of thought: Attaching importance to personal opinions, solving given problems, and earning the approval of others. Bullard's proposed alternatives don't look very good to me, but Bullard has surely identified some important problems.
I can think of other school-inculcated bad habits of thought, too many to list, but I'll name two of my least favorite.
I suspect the most dangerous habit of thought taught in schools is that even if you don't really understand something, you should parrot it back anyway. One of the most fundamental life skills is realizing when you are confused, and school actively destroys this ability - teaches students that they "understand" when they can successfully answer questions on an exam, which is very very very far from absorbing the knowledge and making it a part of you. Students learn the habit that eating consists of putting food into mouth; the exams can't test for chewing or swallowing, and so they starve.
Much of this problem may come from needing to take three 4-credit courses per quarter, with a textbook chapter plus homework to be done every week - the courses are timed for frantic memorization, it's not possible to deeply chew over and leisurely digest knowledge in the same period. College students aren't allowed to be confused; if they started saying, "Wait, do I really understand this? Maybe I'd better spend a few days looking up related papers, or consult another textbook," they'd fail all the courses they took that quarter. A month later they would understand the material far better and remember it much longer - but one month after finals is too late; it counts for nothing in the lunatic university utility function.
Many students who have gone through this process no longer even realize when something confuses them, or notice gaps in their understanding. They have been trained out of pausing to think.
I recall reading, though I can't remember where, that physicists in some country were more likely to become extreme religious fanatics. This confused me, until the author suggested that physics students are presented with a received truth that is actually correct, from which they learn the habit of trusting authority.
It may be dangerous to present people with a giant mass of authoritative knowledge, especially if it is actually true. It may damage their skepticism.
So what could you do? Teach students the history of physics, how each idea was replaced in turn by a new correct one? "Here's the old idea, here's the new idea, here's the experiment - the new idea wins!" Repeat this lesson ten times and what is the habit of thought learned? "New ideas always win; every new idea in physics turns out to be correct." You still haven't taught any critical thinking, because you only showed them history as seen with perfect hindsight. You've taught them the habit that distinguishing true ideas from false ones is perfectly clear-cut and straightforward, so if a shiny new idea has anything to recommend it, it's probably true.
Maybe it would be possible to teach the history of physics from a historically realistic point of view, without benefit of hindsight: show students the different alternatives that were considered historically plausible, re-enact the historical disagreements and debates.
Maybe you could avoid handing students knowledge on a silver platter: show students different versions of physics equations that looked plausible, and ask them to figure out which was the correct one, or invent experiments that would distinguish between alternatives. This wouldn't be as challenging as needing to notice anomalies without hints and invent alternatives from scratch, but it would be a vast improvement over memorizing a received authority.
Then, perhaps, you could teach the habit of thought: "The ideas of received authority are often imperfect but it takes a great effort to find a new idea that is better. Most possible changes are for the worse, even though every improvement is necessarily a change."
Maybe I was lucky to have "better than average" teachers, or maybe the french school system is a quite different from the US one, but I remember several counter-example to those problems from my high school and university time, in maths, physics, chemistry and biology, I'll tell one example from each.
In maths, we were often asked to figure by ourselves (intuitively at least) if a "theorem" would be true or not, before being a proof of it being true to false.
In physics, we were given experimental results and asked to draft what law could the results follow. It lacked the "devise new experiments to test your law" part, but it's still better than nothing.
In chemistry, we were once given a substance (potassium permanganate, but we weren't told what it was) and a set of solutions, and we were told the substance was used to test solutions, but not how, and we had to figure out what it could test (acidity).
And in biology, in genetics, it wasn't uncommon to give us some experimental results over generations, and ask us to devise the way a given characteristic was reflected in gene (using one or two gene, on sexual chromosome or not, dominant or not, ...). I remember even being told "try to make a law on part on the data, and then test it on the rest of the data", which is close as we can get to real experimental method on paper.
Another one in biology was a very interesting "proof" of evolution : we had two boxes, on each we were putting cotton with water and sugar, a pill of antibiotics in one side, and some bacteria in the other side. One box was to be exposed to UV light for a light while every day, the other not. Then we had two weeks to explain what will happen and how, and after we explained the predicted outcome, we would look at the boxes. (In the box that was exposed to UV light, the bacteria colonized everything, but in the one not exposed to UV light, the bacteria couldn't get near the antibiotics. After a few more weeks, the bacteria did spread everywhere in the two boxes).
Also, most of the teachers I had were very receptive and encouraging when pointed to a mistake they did (as long, at least, as the mistake was politely pointed at, not aggressively so), mitigating somewhat the "authority effect".
But I agree that those were rare, not exceptionally rare, but still much less common than the "here is the laws of newton mechanics, now compute the movement of a projectile with that initial speed and direction" or "here are the laws of thermodynamics and the gas state equation, now compute the final temperature of that system in which that compression was done". Which is better than pure "guessing the password", since you've to apply the laws and do computation, but which are still "here is the truth, apply it".
And I definitely would like we had more of those few examples, they were teaching much more than just giving the answer.
I feel similarly about my high school general science class. The teacher tried to make it hands-on etc. by having us run experiments and do simple engineering within the theme of the current topic, but a. he rarely explained the prerequisites to the projects and b. he still treated them as "one right answer", and you would receive a poor grade if your experiment had odd results or your project didn't meet the standards.