Just found out that the man my ex married was arrested for domestic abuse and pleaded "no contest" to in 2005. Is this the same as a conviction? We have joint/shared custody of our children. Is this something I should pursue legally?
If that is the case, then you probably wouldn't get anywhere legally. A no contest plea was probably part of a plea bargain, and for a prosecutor to agree to that, probably means that the prosecutor wasn't too excited about the case.