Ineptitude is a lack of skill, ability, or competence. A doctor would prove his ineptitude at practicing medicine if he mistakenly removed a patient's spleen instead of his kidney.
Ineptitude and incompetence are synonyms to describe people who have absolutely no idea what they're doing. It's definitely not a quality you'd want in a pilot, who might prove his ineptitude by sending a plane full of passengers hurtling to the ground. Ineptitude also isn't a good quality to have in fields like medicine, where even one careless mistake could be life-threatening.