The actors do fine jobs. Patricia Arquette is believable as a woman who suddenly finds her life turned upside down by occurrences she doesn't understand. Gabriel Byrne plays Andrew like a real person with deep convictions, but also a sense of uncertainty. He is trapped between his duties as a scientist and his responsibilities as a priest. We realize from the beginning that he's involved in some sort of conspiracy.
Corruption is shown to exist at high levels.
Groups wishing to picket and boycott Stigmata certainly have a right to do so, but their efforts would be more productive if directed at a legitimate social problem rather than used to prevent people from seeing this surprisingly unexploitative and unconventional effort.