Pros
Your experience at WHO HQ will be very contingent on the office culture in your department, but as an intern, you will definitely gain a lot of exposure to the day-to-day operations of a large-scale international organization, interact with a very diverse staff and gain access to an incredible array of contacts (ranging from doctors to economists and former policymakers). Generally, the staff in any given department/unit tends to be passionate about and dedicated to the field global health and social justice. Your teamwork, cross-cultural communication and technical competency is likely to increase appreciably.
Cons
As an intern, you might receive some guidance from your supervisor, but this is highly variable and may not be possible at times (esp. if your supervisor is on duty travel frequently). Also, unlike many private sector firms, WHO internships are unpaid and do not, in any way, map onto increased employment opportunities at WHO HQ or its Regional Offices.