The Medical Stuff.
Poitier examines Widmark's brother and suspects a brain tumor. He examines his retina and then gives the patient a spinal tap. After that, the story makes it sound as if Poitier made a mistake, that his might have misdiagnosed the tumor, that he might have been "wrong," as Dr. Warden and the pathologist put it.
That's not how it works though. If the patient presents with a superficial gunshot wound but shows additional symptoms of a brain tumor -- disorientation, a swollen optic nerve disk, signs of intracranial pressure -- any responsible doctor would do the tests that Poitier did, if only to rule out a diagnosis of brain tumor. The only "mistake" would be in NOT doing the tests.
Instead of Dr. Warden saying (twice) that any good doctor might have done what Poitier did, he would have said that any good doctor SHOULD have done what Poitier did. As it stands, the tension is hyped but the medical stuff gets twisted into a fake contrast between "right" and "mistaken."