Do mri, ct, and ultrasound fail to detect cancer or fungal infection?

You need to be more specific. Fungal infections require microscopic examination of tissue and culture. Some cancers like leukemia do not show up on any imaging. Imaging studies identify lesions that need to be excised or biopsied for tissue examination by a pathologist for the actual diagnosis.

Infections are not picked by imaging studies most of the times, but by the combination of symptoms and cultures. Early solid cancers can be also missed by imaging studies.