Is it a sin for church members to watch tv shows like "Dancing with the Stars?"
I have never seen the show referenced, but then I rarely watch television, so I'll address the problem of watching dancing.
One of the problems with many dances is that they are designed to excite lust both in the participants and in the viewers. Some dances feature moves that imitate sexual actions. If a dance is wrong to participate in because of what it portrays or because of what it promotes in a participant, it would also be wrong to promote by viewing. "Who, knowing the righteous judgment of God, that those who practice such things are deserving of death, not only do the same but also approve of those who practice them" (Romans 1:32).
For a discussion concerning dancing itself, see "Dancing in the Bible"