micky wrote:
I'm only acquainted with car inspection in Pa.and Md. but on TV I saw a
woman who bougght a used car, found out that the heater core was
leaking, and didn't take it for inspection until after she fixed the
heater.

Is there any state where that would cause a car to fail inspection?

Not enough information.
However, ANY leaks that were noticeable in any vehicle system would fail
the Texas inspection. Texas does not take the car apart for inspections
like in other states though. Nothing is removed.