Is a woman's work as a doctor haram if it involves extensive mixing with men and there are non-committed female doctors, or is there a dispensation for her in this due to the need for committed female doctors?

There is no impediment to a woman working as a doctor if she adheres to Islamic guidelines, whether the need is personal or societal, such as society's need for a trustworthy and committed female doctor. The issue revolves around the benefit realized from a woman's work. If a benefit exists and the work adheres to Islamic guidelines, then it is permissible. As for mixing (of genders), no hospital is free of it, but a Muslim woman must be careful not to touch a non-mahram (definition) man, or be overly familiar with him, or speak to him without need, or be alone with him.