Pros
The people tend to be bright, and the occasional dummy who slips in is usually weeded out quickly. Some of the managers are fabulous people, who really care about their employees and watch out for their interests. You'll learn a ton working at Clorox, too. Finally, the products are cool, and it's easy to be proud of the fact that you work at a well-established & innovative* company with a great brand name. *Some are sure to be baffled by my "innovative" comment, but I think Clorox is very innovative. GreenWorks, Kingsford SureFire, and the new carbon-blended litter are just some of the examples that come to mind.
Cons
While some managers are fabulous, I would argue that the majority don't really care about their employees. Many are too busy trying to advance their own agendas to worry about what their employees need. Work/life balance can suck, too, although to some degree it depends on your personality -- are you naturally a hard worker? Clorox will sometimes take advantage of people who naturally go above and beyond. It pays to look out for yourself, because at the end of the day, nobody else will. That's pretty typical anywhere, though, isn't it?