A very intelligent but irrational person is easy to show, but a rational yet dumb one seems much harder to me. I suppose you could ham-fist it by making them suck at various intellectual challenges - any better ideas?

I thought early Bella from Luminosity did a pretty good job at showing someone rational but with no special cognitive abilities (we're talking about averages, here, not idiots). She just had noticed her limitations and practiced at overcoming them, but that by itself was very good at making her more effective.

One of the simplest author tricks I can come up with is to give your character a thought speed and stick to it. Harry seems to run through ten lines of text in seconds, sometimes, but if you go with, say, your speed reading aloud you can get a reasonable estimate of how long it takes an average person to ponder something. People can mention how they zone out; they can miss opportunities; they can not come up with a good enough solution in time. They can make conscious decisions about what they will and will not think about.

Stubbornly refusing to believe in magic.

Stubbornly agreeing with an outside view prediction even when faced with many convincing arguments why this example is special, if most examples are expected to have similarly convincing arguments.

Stubbornly refusing to consider solutions to a problem before examining it more carefully.

Quickly changing opinion when faced with a valid argument, even though it "should" be emotionally unconvincing.