> how do you reliably detect that one of them is bent or installed incorrectly

During standard pre-launch or manufacturing tests. It should be verified by applying some change and checking that this change is measured correctly.

Generally for critical sensors, you can add some circuitry or even mechanical means of checking (eg heater on temperature sensor). If mechanical side fails, whole sensor module is marked as failed. Critical sensors should be designed in a way that you know when it fails.

For many sensors especially critical ones there are multiple independent ones (like indicated airspeed). If they deviate there are standard procedures to determine which one(s) are faulty. For IAS you basically set a determined thrust at a determined pitch. Then you have a table which gives you IAS for the altitude you are at. This will determine the faulty pitot tube. I think for other sensors there are similar procedures.

You can also have 3 sensors and use a simple 2 of 3 check. The likeliness of 2 failing at the same time would probably be pretty low.