On the other side, measles and rubella can be fatal for healthy children. The statistics on the CDC site is that mortality for measles is one out of 1000. For rubella, while it isn't usually fatal for children, children spread it to pregnant women. The virus then causes heart defects, deafness and mental retardation in their babies.
Protecting children from all diseases is thought to promote the development of allergies - the "hygiene hypothesis." No doctor I know of or have heard of recommends exposing children to measles, mumps or rubella to avoid this, however. Older siblings, pets, and colds are a better choice.
Not quite true. Well over 90% of cervical cancer cases are caused by one of a number of HPV strains. Gardasil protects against the two strains most commonly associated with cervical cancer (along with two other strains associated with genital warts), and it's those two common strains that account for about 70% of cervical cancer cases. That means 20%+ of remaining cases are caused by a variety of rarer HPV strains that Gardasil doesn't target.