I find their beliefs horrendous. Their rigid views on gender roles are quite appalling, IMO. The older girls live at home, without any real opportunities for a meaningful life outside the family, waiting for the right young man to approach their father and ask permission to "court" them. Shudder.
Also, none of the children (boys or girls) are encouraged to pursue higher education. It seems as though their formal education is extremely limited, which I suppose makes a certain kind of depressing sense if you want to raise children not to question the circumscribed life they are leading (see also the Amish for a similar philosophy).
The Duggar family claims to lead a life far removed from all the scary influence of the secular world, and yet they place themselves smack in the middle of one of the trashiest possible manifestations of pop culture (reality T.V.) with their own show. I wonder how they explain that to themselves.
I'm really uncomfortable with parents putting their children into the position of being part of an ongoing reality T.V. program. They couldn't afford to pay for the gigantic house they were building until the network ponied up the cash. And now they happily accept all sorts of money, free trips, etc., while putting their children on display for the entertainment of the viewers. I think it is exploitation of those kids, plain and simple, and basically equivalent to the Dionne quintuplets, just updated with current technology.
I can imagine Johanna (now aged about 6 and quite a little spitfire) turning out to be the family rebel and writing a tell-all book some day.