This show was, in many ways, my childhood. It's clean (the worst you'll see is one or two uses of the H word from Uncle Jesse, only in one season, and Dad covers the kids' ears). The girls are sweet, the three dads do their best to be gentle, yet authoritative parents, and Aunt Becky is a sweet, strong mother figure. Problems are common to kids and teens, and though it is cheesy that they get solved in thirty minutes, this is a refreshing change from today's sitcoms, where extramarital affairs, drinking, bathroom humor, and questionable morals abound. The humor, too, is lighthearted, fun, and yes, actually funny.
For kids younger than 7: know your child. Most episodes are harmless, but some go a little deeper (one deals heavily with the death of Great-Grandpa, one deals with Alzheimer's, etc). It's also worth noting that little Michelle, while not inherently "bad," is somewhat spoiled as the baby of the family and gets away with behavior some parents may raise an eyebrow at. Jesse's status as a "player" is handled with extreme discretion, but Judeo-Christian parents may raise eyebrows, too. (He's never shown sleeping with anyone but Becky, after marriage, and told up-front that female guests are not allowed overnight).
In short, join the Tanner family, and remind yourself what family is supposed to look like.